More precisely, my question is, Is the wilson loop used to calculate the heavy quark potential always positive in the lattice simulation?(adsbygoogle = window.adsbygoogle || []).push({});

(i) as we are usually told, wilson loops of the following form are related with

the heavy quark potentials

..........................................

_________ <WC_______.........

|...............................|../\ ...

|WD................../\......|...|....

|...............................|...r....

| \/...................WB....|...|....

|_____WA>__________|..\/....

<---------- t ----------->.........

..........................................

<W>=<W_{r,t}> ~ e^{-V( r )*t}

so we expect <W> is always positive(or negative,

any way, it should not change signs we we change t and r)

(ii) but by definition

<W>= <tr[e^{iAa ta} * e^{i Ab tb} * e^{-iAc tc} * e^{-i Ad td}]>

= <tr[WA * WB * WC * WD]>

since in numerical simulations, the link variables WA, WB, WC, WD et al

are random unitary matrix, we cannot expect the trace of their products

is positive.

I encounter this problem because in one of my little exercises to write

lattice QCD codes, I got results just as I explained in (ii), so I cannot extract

the heavy quark potentials, because some times I get W(r,t)>0, some times

W(r,t)<0. Especially worse is, I encounter the case

W(r,t)>0

W(r,t+a)<0

So the proportion W(r,t+a)/W(r,t) ~ e^{-V( r )*a} < 0, this is really a disappointing

outcome.

What key points did I ignored ? Who can tell me or give me some

hints? If you have comments or remarks, please do not hesitate to reply this

thread or write me email, dfzeng2000@hotmail.com

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# Is the wilson loop always positive in the lattice simulation?

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