Skip to main content

TT OPE for bc ghosts and massless fermions

While calculating T(z) T(w) OPE for bc ghosts and massless fermions I came across a weird result.

I could get the central charge correct and also the T(w)/(z-w)^2 term correct but the other terms which remain does not add up to T(w) as expected.

In massless fermion case:

T = :ψ ψ:

T(z) T(w) = 1/4/(z-w)^4 + T(w)/(z-w)^2 + ( 1/2 ψ ∂2 ψ + ∂ ψ ∂ ψ )/(z-w)

But,
∂ T = ψ ∂2 ψ + ∂ ψ ∂ ψ

So, I cannot account for the 1/2 factor in front of ψ ∂2 ψ .

In bc ghost case :

T = : 2 c b + c b :

T(z) T(w) = 1/4/(z-w)^4 + T(w)/(z-w)^2 + ( 4 ∂2c b + 3 ∂c ∂b - c ∂2b)/(z-w)

But,
∂T = 2 ∂2c b + 3 ∂c ∂b + c ∂2b

This means I have some terms like

T(z) T(w) = 1/4/(z-w)^4 + T(w)/(z-w)^2 + ( 4 ∂2c b + 3 ∂c ∂b - c ∂2b)/(z-w)
= 1/4/(z-w)^4 + T(w)/(z-w)^2 + [∂ T + 2( ∂2c b - c ∂2b)]/(z-w)
= 1/4/(z-w)^4 + T(w)/(z-w)^2 + ∂ [ T + 2 ( ∂c b - c ∂b) ]/(z-w)

I have no idea why the term ( ∂c b - c ∂b) should be zero.

So the problem is:
1. Whether it is correct to directly differentiate expression for T(z) to get the ∂T(z) ?
2. Is there a way to discard the total derivative using EOM or Belinfante tensor ..?

I have no idea still.

Comments

Popular posts from this blog

Fastest way to send multiple drafts from gmail

People claim that the fastest way to send multiple email drafts is to use Gmail IMAP with email client like Outlook or Evolution or Thunderbird. But I have found this is not true. Because Thunderbird and Evolution etc. email clients treats the drafts as emails still to be edited. So it is not just simple select all and hit send. Each email draft has to be opened and sent separately. That is a lot of clicks and mouse movements, wasting precious time and energy. I have a better solution which involves minimum keystrokes and mouse usage. Efficiency booster technique for sending emails. If someone is feeling adventurous and want to try it from the Gmail interface itself, here's how to do it in the fastest possible manner. It involves using the mouse once. Select the first draft. Gmail would open a new email box and put the cursor inside the box to write. Press TAB once to go the Send button. Press ENTER to send. Now Gmail sends it and the box is gone but the highlight goes to the last

LYRICS OF CHANDRABINDOO

___________________________________________________________________ SWEET HEART FROM AAR JAANI NAA(T-SERIES) -- SWEETHEART -- Pratham college-er din ta Aajo thik e mone poRey scene ta Dada didi haath dhorey siNRi tei bose poRey Aamar chokh ta ghorey bon bon bon bon Sweetheart, I am seating alone Sweetheart, for me there is none DhoNk gile chole gelo pratham maas Meye dekhlei feli deergho-shwash DhoNk gile chole gelo pratham maas Meye dekhlei othe nabhishwash Meyera bheeshan smart poRey chhoto mini-skirt Aamar e je sheet korey kon kon kon kon Sweetheart, I am seating alone Sweetheart, for me there is none Taarporey kete gelo maas chaar Fuse holo je kato future Bandhura purse khule eke oke taake tole Aamar pran ta korey chon mon chon mon Sweetheart, I am seating alone Sweetheart, for me there is none Ekdin lawn theke beriye Ek tanayaar dike taakiye Hawt korey ki je holo magaj ta ghurey gelo Taar kaaner saamne kori ghyan ghyan ghyan ghyan Sweetheart, I am seating alone Sweethea

Changing the font size of section headings in LaTex

You have several ways to do so: 1.- A direct redefinition of \section: \makeatletter \renewcommand\section{\@startsection{section}{1}{\z@}%                                   {-3.5ex \@plus -1ex \@minus -.2ex}%                                   {2.3ex \@plus.2ex}%                                   {\normalfont\large\bfseries}} \makeatother 2.- By means of the titlesec package: \usepackage{titlesec} \titleformat{\section}{\large\bfseries}{\thesection}{1em}{} 3.- By means of the sectsty package: \usepackage{sectsty} \sectionfont{\large} source : http://www.latex-community.org/forum/viewtopic.php?f=4&t=3245   Now, I would explain the titlesec package a bit more (because it seems easier to me and with more options) : To change the section fonts with this package put the following lines in the preamble - \usepackage{titlesec} \titleformat{\ section }{\ large \ bfseries }{\thesection}{1em}{} Options available are- a> Font size - \normals