% This is the metafont for the feynfont font, release 0.4.3, 2022 July 20 % % Copyright 1991, 1994, 2001, 2002, 2005, 2008-10, Norman Gray. % See the file LICENCE for licence details. % % Mercurial revision 0a471f8ed572, 2022-07-20 11:23 +0100, tag 0.4.3 + 0 % % % % When I look at the property list of the generated TFM (using % tftopl) it starts with `(FAMILY CMR)': but this isn't in the cmr % family. I can't find anything in cmbase.mf which would cause % this. Perhaps I need to read the Metafont Book more closely. mode_setup; font_setup; % a# is the position of the characters above the baseline. a# := on_math_axis * math_axis#; % math_axis is defined by cmr % Feyn macros input feynmac; define_pixels (module,bigarrow,littlearrow,blobr,a); define_blacker_pixels (linewidth,thinlinewidth); pickup pencircle scaled linewidth; diagram_pen := savepen; % general definitions phangle := 75; % photon angle squash := 0.75; % the amount by which some loops are squashed % The caller must set the following parameters to values such as these %boson_wiggles := 4; %this must be an even number %boson_wiggles_loop_small := 4; %boson_wiggles_loop_normal := 6; %boson_wiggles_loop_large := 8; % All the character positions between 0 and hex"7F" % have characters in them. Not all of these characters are ones % which should appear on paper; some (such as `s' or `l') only % appear in ligatures, and others shouldn't appear at all. If, % however, there are no characters in these positions, some DVI % readers (including TFtoPL and OzTeX for example) complain about a % `bad TFM file'. These locations are therefore occupied by the % character generated by the errorchar macro, which is 0pt wide, and % 1module# high. This character doesn't generate any real error, % but the glyph will be manifestly peculiar on paper. % % Add code to extra_beginchar so that we keep a record of all the % characters that we generate, so that we can generate an errochar % character for each of the codepoints that we've skipped. `charcode' % is defined in the expansion of beginchar() numeric donechar[]; string donecharerror; donecharerror := "Duplicate character"; extra_beginchar := extra_beginchar & "if known donechar[charcode]: errmessage donecharerror; fi donechar[charcode] := 1;"; path charpath, charpathb; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % Digits 0x30--0x39. Obtain these from the cmr source file: romand.mf. input romand; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % Fermions def path_fermion (expr scale_sharp, ang) = begingroup save scale; scale := hround(scale_sharp*hppp); if ang > 0: % slopes upward (0,a) .. (scale*(cosd ang), scale*(abs sind ang)+a) else : (0,scale*(abs sind ang)+a) .. (scale*(cosd ang), a) fi endgroup enddef; threechars ("f", "fermion", path_fermion(2module#, 0), 0.5, 2module#, 0, 0, (0,0.1module), "top"); begingroup % make closed fermion loop, for phi^4 theory clearxy; save height; height# := 2module#; define_pixels(height); z2 = (0, height); %top of loop y1 = y3 = 2y2/3; x1+x3 = 0; x1-x3 = 2height/3; charpath := origin .. z1 .. z2 .. z3 .. origin; threechars ("k", "fermion loop", charpath shifted (0,a), 2, 0, 2module#, 0, 0, "top"); endgroup; beginchar (hex"21", module#, 0, 0); "short fermion"; pen; draw path_fermion(module#, 0); endchar; % The following characters are in boxes the same vertical size as the black % bit of the character, but they project out of the top by an amount equal to % the height of the math axis, and are that same height clear of the bottom % of the box. % %%%% -90 <= ang <= +90, or all hell will break loose threechars ("e", "upward fermion", path_fermion(2module#, 45), 0.5, 2module#*(cosd 45), 2module#*(abs sind 45), 0, 0, "ulft"); threechars ("d", "downward fermion", path_fermion(2module#, -45), 0.5, 2module#*(cosd -45), 2module#*(abs sind -45), 0, 0, "urt"); threechars ("b", "vertically upward fermion", path_fermion(2module#, 90), 0.5, 2module#*(cosd 90), 2module#*(abs sind 90), 0, 0, "urt"); charpath := path_fermion(2module#, 0); beginchar("m", 2module#, 0, 0); "massive fermion"; pen; draw charpath shifted (0,linewidth); draw charpath shifted (0,-linewidth); annotate_at(point 0.5 of charpath shifted (0,linewidth), "top"); endchar; beginchar("M", 2module#, 0, 0); "r-arrowed massive fermion"; pen; draw charpath shifted (0,linewidth); draw charpath shifted (0,-linewidth); drawarrow (bigarrow, point 0.5 of charpath, 0); annotate_at(point 0.5 of charpath shifted (0,linewidth), "top"); endchar; beginchar(byte"m"-hex"60", 2module#, 0, 0); "l-arrowed massive fermion"; pen; draw charpath shifted (0,linewidth); draw charpath shifted (0,-linewidth); drawarrow (bigarrow, point 0.5 of charpath, 180); annotate_at(point 0.5 of charpath shifted (0,linewidth), "top"); endchar; charpath := path_fermion(module#, 0); beginchar(hex"23", module#, 0, 0); "short massive fermion"; pen; draw charpath shifted (0,linewidth); draw charpath shifted (0,-linewidth); %drawarrow (littlearrow, point 0.5 of charpath, 0); annotate_at(point 0.5 of charpath shifted (0,linewidth), "top"); endchar; begingroup clearxy; save width; width# := 4module#; define_pixels(width); x2-x0 = 2(x1-x0) = width; x1 = 0; y0 = y2 = 0; y1 = 2squash*module; charpath := z0 .. z1 .. z2; threechars("l", "fermion loop", charpath shifted (0,a), 1, 0, 2squash*module#+a#, 0, 0, "top"); threechars("n", "fermion loop, inverted", charpath yscaled -1 shifted (0,a), 1, 0, a#, 0, 0, "bot"); threechars("o", "fermion loop, small", charpath scaled 0.66667 shifted (0,0.66667a), 1, 0, module#+a#, 0, 0, "top"); threechars("w", "fermion loop, small, inverted", charpath xscaled 0.66667 yscaled -0.66667 shifted(0,0.66667a), 1, 0, module#+a#, 0, 0, "bot"); endgroup; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % Gauge bosons % def path_boson (expr scale_sharp, ang, taper) = begingroup save scale; clearxy; scale := hround(scale_sharp*hppp); x1 = 0; x99 = scale*(cosd ang); if ang > 0 : % slopes upward y1 = a; y99 = scale*(abs sind ang) + a; else : y1 = scale*(abs sind ang) + a; y99 = a; fi for i = 3 upto boson_wiggles: z[i] - z[i-1] = z2-z1; endfor z99 - z[boson_wiggles] = z2-z1; def ::(expr b) = {dir (ang+b)} looselink {dir (ang-b)} enddef; z1 ::(phangle)z2 for i = 3 step 2 until boson_wiggles: ::(-phangle) z[i] ::(phangle)z[i+1] endfor if taper <> 0 : {dir (ang-phangle)} .. tension 1 and 0.8 .. {dir (ang+phangle/2)} else : ::(-phangle) fi z99 endgroup enddef; % the following is a simpler version of the above, without the % boson_wiggles, to document what it's supposed to be doing def path_boson_orig (expr scale_sharp, ang, taper) = begingroup save scale; clearxy; scale := hround(scale_sharp*hppp); x1 = 0; x5 = scale*(cosd ang); if ang > 0 : % slopes upward y1 = a; y5 = scale*(abs sind ang) + a; else : y1 = scale*(abs sind ang) + a; y5 = a; fi z2-z1 = z3-z2 = z4-z3 = z5-z4; def ::(expr b) = {dir (ang+b)} looselink {dir (ang-b)} enddef; z1 ::(phangle) z2 ::(-phangle) z3 ::(phangle) z4 if taper <> 0 : {dir (ang-phangle)} .. tension 1 and 0.8 .. {dir (ang+phangle/2)} else : ::(-phangle) fi z5 endgroup enddef; threechars ("g", "gluon", path_boson(2module#, 0, 0), boson_wiggles/2, 2module#, 0, 0, (0, 0.2module), "top"); threechars ("u", "upward gluon", path_boson(2module#, 45, 0), boson_wiggles/2, 2module#*(cosd 45), 2module#*(abs sind 45), 0, 0, "ulft"); threechars ("v", "downward gluon", path_boson(2module#, -45, 0), boson_wiggles/2, 2module#*(cosd -45), 2module#*(abs sind -45), 0, 0, "urt"); threechars (hex"7D", "vertical gluon", path_boson(2module#, 90, 1), boson_wiggles/2, 0, 2module#, 0, 0, "urt"); % plus or minus phangle, depending on whether n is odd or even def pm_angle(expr n) = if odd n: -1 else: 1 fi*phangle enddef; % a gluon quarter loop, in the upper-right quadrant: % wid: radius of loop in modules % nopts: number of points % inv: if 1, the loop goes from the axis to the top; % if 0, from the top down to the axis % negang: if 1, negate the photon angle (so it wiggles oppositely); % if 0, don't % taper: if 1 or 3, the line tapers as it approaches the axis % if 2 or 3, the line tapers as it approaches the top % if 0, the line does not taper % (I can't help feeling this macro has become more complicated than it % really need be...) def path_quadloop (expr wid, nopts, inv, negang, taper) = begingroup save halfwidth, myangle; clearxy; halfwidth# := wid*module#; define_pixels(halfwidth); myangle = if negang <> 0: -phangle else: phangle fi; z0 = (halfwidth, 0); % z0 is on the axis for x = 1 upto nopts: z[x] = z0 rotated (x*90/nopts); endfor if inv = 0: def ::(expr p,ang) = p{p rotated(-90-ang)} looselink enddef; if (taper = 2) or (taper = 3): z[nopts]{dir(0-myangle/2)} .. tension 0.8 and 1 .. else: ::(z[nopts], pm_angle(nopts+negang)) fi for x=nopts-1 downto 2: ::(z[x], pm_angle(x+negang)) endfor if (taper = 1) or (taper = 3): z[1]{z[1] rotated(-90+myangle)} .. tension 1 and 0.8 .. {dir -(90+myangle/2)} else: ::(z[1], pm_angle(1+negang)) fi z0 else: def ::(expr p,ang) = looselink {p rotated (90+ang)}p enddef; if (taper = 1) or (taper = 3): z0 {dir (90+myangle/2)} .. tension 0.8 and 1 .. z[1]{z[1] rotated(90-myangle)} else: z0{dir (90+myangle)} ::(z[1], pm_angle(1+negang)) fi for x=1 upto nopts-1: ::(z[x], pm_angle(x+negang)) endfor if (taper = 2) or (taper = 3): .. tension 0.8 and 1 .. {z[nopts] rotated (90+myangle/2)}z[nopts] else: ::(z[nopts], pm_angle(nopts+negang)) fi fi endgroup enddef; % next_odd: evaluate to the next odd number greater than or equal to n def next_odd(expr n) = (2*floor(n/2)+1) enddef; threechars ("q", "gluon, quadrant 1", path_quadloop(2, boson_wiggles_loop_normal, 1, 0, 3) xscaled -1 shifted (0,a), next_odd(2boson_wiggles_loop_normal/3), 0, 2module#, 0, % height is 2module#, not 2module#+a#, so that % they line up OK in \Diagram 0, "ulft"); threechars ("r", "gluon, quadrant 2", path_quadloop(2, boson_wiggles_loop_normal, 0, 0, 3) shifted (0,a), next_odd(boson_wiggles_loop_normal/2), 0, 2module#, 0, 0, "urt"); threechars ("s", "gluon, quadrant 3", path_quadloop(2, boson_wiggles_loop_normal, 0, 1, 3) yscaled -1 shifted (0,a), next_odd(boson_wiggles_loop_normal/2), 0, a#, a#-2module#, 0, "lrt"); threechars ("t", "gluon, quadrant 4", path_quadloop(2, boson_wiggles_loop_normal, 1, 1, 3) scaled -1 shifted (0,a), next_odd(2boson_wiggles_loop_normal/3), 0, a#, a#-2module#, 0, "llft"); % The two loops following have the annotation off-centre, to keep % it clear of the wiggles. Would it look better being "top" and "bot" % again, but with a non-zero offset in the second-last argument? % These two are vertically squashed so that they take up less than 2 % modules vertically, which means in turn that {gl glu} can sit in a % two-loop diagram without crashing into the baseline. threechars ("y", "gluon half loop", ((path_quadloop(2, boson_wiggles_loop_normal, 1, 0, 1) xscaled -1) .. path_quadloop(2, boson_wiggles_loop_normal, 0, 0, 1)) yscaled squash shifted (0,a), boson_wiggles_loop_normal+1, 0, 2squash*module#+a#, 0, 0, "urt"); threechars ("z", "gluon half loop, inverted", ((path_quadloop(2, boson_wiggles_loop_normal, 1, 1, 1) scaled -1) .. (path_quadloop(2, boson_wiggles_loop_normal, 0, 1, 1) yscaled -1)) yscaled squash shifted (0,a), boson_wiggles_loop_normal+1, 0, a#, a#-2module#, 0, "llft"); % Small and large boson half loops are at positions which are not characters. % That's OK -- they can still be accessed by ligatures. % 7b='{', 7c='|' threechars (hex"7B", "large gluon half loop", ((path_quadloop(2.66667, boson_wiggles_loop_large, 1, 0, 1) xscaled -1) .. path_quadloop(2.66667, boson_wiggles_loop_large, 0, 0, 1)) shifted (0,a), 1.5boson_wiggles_loop_large, 0, 2.66667module#+a#, 0, 0, "urt"); threechars (hex"7C", "small gluon half loop", ((path_quadloop(1.3333, boson_wiggles_loop_small, 1, 0, 1) xscaled -1) .. path_quadloop(1.3333, boson_wiggles_loop_small, 0, 0, 1)) shifted (0,a), 1.5boson_wiggles_loop_small, 0, 1.3333module#+a#, 0, 0, "llft"); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % Ghosts ghost_points = 2(boson_wiggles + 1); % should be at least 8? def draw_ghost(expr a, b, apos) = begingroup % pattern for ghost_points=10: "-_--_--_--_-" clearxy; z1 = a; z[ghost_points] = b; z2-z1 = z[ghost_points]-z[ghost_points-1]; for i = 2 step 2 until (ghost_points-1): z2-z1 = z[i+1]-z[i]; endfor z4-z3 = 2(z2-z1); for i = 5 step 2 until (ghost_points-2): z4-z3 = z[i+1]-z[i]; endfor pen; draw z1--z2; draw z[ghost_points-1]--z[ghost_points]; for i = 3 step 2 until (ghost_points-2): draw z[i]--z[i+1]; endfor annotate_at(0.5[z1,z[ghost_points]], apos); endgroup enddef; % the following is a simpler version of the above, without the % ghost_points parameter, to document what it's supposed to be doing def draw_ghost_orig(expr a, b, apos) = begingroup clearxy; z1 = a; z10 = b; z4-z3 = 2(z2-z1); z4-z3 = z6-z5 = z8-z7; z2-z1 = z3-z2 = z5-z4 = z7-z6 = z9-z8 = z10-z9; pen; draw z1..z2; draw z3..z4; draw z5..z6; draw z7..z8; draw z9..z10; annotate_at(0.5[z5,z6], apos); endgroup enddef; beginchar ("h", 2module#, 0, 0); "ghost"; pen; draw_ghost((0,a), (w,a), "top"); endchar; beginchar (byte "h"-hex"20", 2module#, 0, 0); "r-arrowed ghost"; pen; draw_ghost((0,a), (w,a), "top"); drawarrow (littlearrow, .5[(0,a), (w,a)], 0); endchar; beginchar (byte "h"-hex"60", 2module#, 0, 0); "l-arrowed ghost"; pen; draw_ghost((0,a), (w,a), "top"); drawarrow (littlearrow, .5[(0,a), (w,a)], 180); endchar; beginchar ("i", 2module#*(cosd 45), 2module#*(sind 45), 0); "upward ghost"; pen; draw_ghost((0,a), (w,h+a), "ulft"); endchar; beginchar (byte"i"-hex"20", 2module#*(cosd 45), 2module#*(sind 45), 0); "r-arrowed upward ghost"; pen; draw_ghost((0,a), (w,h+a), "ulft"); drawarrow (littlearrow, .5[(0,a), (w,h+a)], 45); endchar; beginchar (byte"i"-hex"60", 2module#*(cosd 45), 2module#*(sind 45), 0); "l-arrowed upward ghost"; pen; draw_ghost((0,a), (w,h+a), "ulft"); drawarrow (littlearrow, .5[(0,a), (w,h+a)], 45+180); endchar; beginchar ("j", 2module#*(cosd 45), 2module#*(sind 45), 0); "downward ghost"; pen; draw_ghost((0,h+a), (w,a), "urt"); endchar; beginchar (byte"j"-hex"20", 2module#*(cosd 45), 2module#*(sind 45), 0); "r-arrowed downward ghost"; pen; draw_ghost((0,h+a), (w,a), "urt"); drawarrow (littlearrow, .5[(0,a), (w,h+a)], -45); endchar; beginchar (byte"j"-hex"60", 2module#*(cosd 45), 2module#*(sind 45), 0); "l-arrowed downward ghost"; pen; draw_ghost((0,h+a), (w,a), "urt"); drawarrow (littlearrow, .5[(0,a), (w,h+a)], -45+180); endchar; % ghost loops begingroup clearxy; clearit; % clear current picture picture ghostloop; pair refpt, arrowpoint; refpt := (-2module, 0); for i=0 upto 23: z[i] = refpt rotated -(i/24*180) yscaled squash shifted (0,a); endfor arrowpoint := z[12]; transform below; below := identity rotatedaround ((0,a), 180); pen; for i=0 step 2 until 22: draw z[i]--z[i+1]; endfor ghostloop := currentpicture; clearit; beginchar (hex"7E", 0, 2squash*module#+a#, 0); "ghost loop"; addto currentpicture also ghostloop; annotate_at(arrowpoint, "top"); endchar; beginchar (hex"7E"-hex"20", 0, 2squash*module#+a#, 0); "r-arrowed ghost loop"; addto currentpicture also ghostloop; drawarrow(littlearrow, arrowpoint, 0); annotate_at(arrowpoint, "top"); endchar; beginchar (hex"7E"-hex"60", 0, 2squash*module#+a#, 0); "l-arrowed ghost loop"; addto currentpicture also ghostloop; drawarrow(littlearrow, arrowpoint, 180); annotate_at(arrowpoint, "top"); endchar; beginchar (hex"7F", 0, a#, 0); "ghost loop, inverted"; addto currentpicture also ghostloop transformed below; annotate_at(arrowpoint transformed below, "top"); endchar; beginchar (hex"7F"-hex"20", 0, a#, 0); "r-arrowed ghost loop, inverted"; addto currentpicture also ghostloop transformed below; drawarrow(littlearrow, arrowpoint transformed below, 0); annotate_at(arrowpoint transformed below, "top"); endchar; beginchar (hex"7F"-hex"60", 0, a#, 0); "l-arrowed ghost loop, inverted"; addto currentpicture also ghostloop transformed below; drawarrow(littlearrow, arrowpoint transformed below, 180); annotate_at(arrowpoint transformed below, "top"); endchar; endgroup; beginchar (hex"22", module#, 0, 0); "short ghost"; pen; z1 = (0,a); z6 = (w,a); z4-z3 = 2(z2-z1); z2-z1 = z3-z2 = 1/2(z4-z3) = z5-z4 = z6-z5; draw z1..z2; draw z3..z4; draw z5..z6; annotate_at(0.5[z3,z4], "top") endchar; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % Odds and sods beginchar (hex"60", 2module#, 0, 0); "spacer"; endchar; beginchar (hex"40", module#, 0, 0); "short spacer"; endchar; beginchar ("c", 2blobr#, blobr# + a#, blobr#); "complete vertex"; pen; draw (0,a) .. (w,a) .. cycle; annotate_at((w/2,w/2+a), "top"); endchar; %beginchar ("d", module#/2, 0, 0); "weeny fermion"; % pen; % draw (0,a)..(w,a); %endchar; % %beginchar ("k", module#/2, 0, 0); "weeny massive fermion"; % pen; % y1 - a = y2 - a = a - y3 = a - y4 = module#/3.5; % x1 = x3 = 0; % x2 = x4 = w; % draw z1--z2; % draw z3--z4; %endchar; % %beginchar ("l", module#, 0, 0); "short massive fermion"; % pen; % y1 - a = y2 - a = a - y3 = a - y4 = module#/3.5; % x1 = x3 = 0; % x2 = x4 = w; % draw z1--z2; % draw z3--z4; %endchar; %beginchar ("n", 4module#, 2module#-a#, 2module#-a#); % pen; "fermion loop"; % z0 = (0,a); z1 = (w,a); % draw z0{dir phangle} ..tension 1.15.. {dir -phangle}z1; % draw z0{dir -phangle} ..tension 1.15.. {dir phangle}z1; %endchar; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % Other symbols garrow("a", 0, 1); garrow(hex"03", 180, 1); beginchar ("p", 2blobr#, blobr# + a#, blobr# - a#); pen; "proper vertex"; picture p[]; pair t[]; fill (-blobr, 0) .. (blobr, 0) .. cycle; p1 := currentpicture; clearit; draw (-blobr, 0) .. (blobr, 0) .. cycle; p2 := currentpicture; clearit; t1 = 5/6[origin, (0,blobr)] shifted (-blobr, 0); t7 = 5/6[origin, (0,blobr)] shifted (+blobr, 0); forsuffixes s = 2,3,4,5,6 : t[s] = t[s-1] shifted (0, -blobr/3); t[s+6] = t[s+5] shifted (0, -blobr/3); endfor forsuffixes s = 1,2,3,4,5,6,7,8,9,10,11,12 : z[s] = t[s] rotated 45; endfor forsuffixes s = 1,2,3,4,5,6 : draw z[s] -- z[s+6]; endfor addto currentpicture also p1; cull currentpicture keeping (2,2); % & the two pictures addto currentpicture also p2; currentpicture := currentpicture shifted (blobr,a); labels (range 1 thru 12); annotate_at((blobr,blobr+a), "top"); endchar; beginchar ("P", 2blobr#, blobr#+a#, blobr#-a#); % see complete vertex "c" pen; "proper vertex 2"; fill (0,a) .. (w,a) .. cycle;% withcolor black; annotate_at((w/2,w/2+a), "top"); endchar; beginchar ("x", 0, a#, -a#); "counterterm"; pen; -x1 = -x2 = x3 = x4; y1 = -y2 = y3 = -y4; z3 = (2blobr/3, 0) rotated 45; draw z1 .. z4; draw z2 .. z3; currentpicture := currentpicture shifted (0,a); annotate_at(0.5[z1,z3] shifted (0,a), "top"); endchar; beginchar (hex"20", module#, a#, 0); "space block"; pen; message "spacer: width=" & decimal w & ", height=" & decimal h; draw origin--(w,h); draw (0,h)--(w,0); endchar; % Now generate an errorchar() in each of the code positions we've skipped for n = 0 upto hex"7F": if not known(donechar[n]): beginchar (n, 0, module#, 0); errorchar(h); endchar; fi endfor % Construct the ligature tables. ligtable "a" : % arrow "A" =: "a", % right-arrow, for symmetry "V" =: hex"03"; % left-arrow ligtable "f" : % fermion "A" =: "F", % right-arrowed "V" =: hex"06", % left-arrowed "u" =: "e", % upward "d" =: "d", % downward "v" =: "b", % vertical "s" =: hex"21", % short "l" =: "l", % loop "0" =: hex"60"; % spacer ligtable "e" : % upward fermion, fe "A" =: "E", % arrowed "V" =: hex"05"; ligtable "d" : % downward fermion, fd "A" =: "D", "V" =: hex"04"; ligtable "b" : % vertical fermion, fv "A" =: "B", "V" =: hex"02"; ligtable hex"21" : % short fermion "0" =: hex"40"; % short spacer ligtable "k" : % fermion closed loop "A" =: "K", % arrowed "V" =: hex"0b"; ligtable "l" : % fermion loop "u" =: "n", % upside down "o" =: "k", % closed loop (for scalar theory) "S" =: "o", % small "A" =: "L", "V" =: hex"0C"; ligtable "g" : % gluon "A" =: "G", "V" =: hex"07", "u" =: "u", "d" =: "v", "v" =: oct"175", "l" =: "y", % gluon half-loop "1" =: "q", % gluon quarter-loop, 1st quadrant (upper-left) "2" =: "r", % 2nd "3" =: "s", % 3rd "4" =: "t"; % 4th ligtable "m" : % massive fermion "A" =: "M", "V" =: hex"0D", "s" =: hex"23"; ligtable "n" : % inverted fermion "A" =: "N", "V" =: hex"0E"; ligtable "o" : % fermion loop small "u" =: "w", % upside down "A" =: "O", "V" =: hex"0F"; ligtable "q" : % gluon, 1st quadrant "A" =: "Q", "V" =: hex"11"; ligtable "r" : % gluon, 2nd quadrant "A" =: "R", "V" =: hex"12"; ligtable "s" : % gluon, 3rd quadrant "A" =: "S", "V" =: hex"13"; ligtable "t" : % gluon, 4th quadrant "A" =: "T", "V" =: hex"14"; ligtable "u" : % upward gluon "A" =: "U", "V" =: hex"15"; ligtable "v" : % downward gluon "A" =: "V", "V" =: hex"16"; ligtable "w" : % fermion loop, small, upside-down "A" =: "W", "V" =: oct"027"; ligtable oct"175" : % vertical gluon "A" =: oct"135", "V" =: oct"035"; ligtable "y" : % gluon half-loop "A" =: "Y", "V" =: hex"19", "B" =: hex"7B", % large "S" =: hex"7C", % small "u" =: "z"; % ...upside down ligtable hex"7B" : % large gluon half loop "A" =: hex"5B", "V" =: hex"1B"; ligtable hex"7C" : % small gluon half loop "A" =: hex"5C", "V" =: hex"1C"; ligtable "z" : % upside-down gluon loop "A" =: "Z", "V" =: hex"1A"; ligtable "h" : % ghost "A" =: "H", "V" =: hex"08", "u" =: "i", % upward "d" =: "j", % downward "s" =: hex"22", % short "l" =: hex"7E"; % ghost loop ligtable hex"7E" : % ghost loop "A" =: hex"5E", % r-arrowed "V" =: hex"1E", % l-arrowed "u" =: hex"7F"; % upside down ligtable hex"7F" : % ghost loop inverted "A" =: hex"5F", % r-arrowed "V" =: hex"1F"; % l-arrowed ligtable "i" : % upward ghost "A" =: "I", "V" =: hex"09"; ligtable "j" : % downward ghost "A" =: "J", "V" =: hex"0A";