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### BRST quantization and norm

States with definite ghost number have zero norm (since ghost number is anti-hermitian and has real eigenvalues). E.G. when quantizing relativistic point particle, physical spectrum turns out to ...
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### What is a ghost number?

I am currently studying CFT chapter of Becker,Becker,Schwarz and am trying to understand what the ghost number is in BRST Quantization. From what I gather BRST Quantization is used to add an extra ...
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### Ghost in the quantization of relativistic particle

It is well known that in the quantization of certain relativistic theories such electromagnetism or relativistic string negative norm states could arise when quantizing covariantly. Acting with ...
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### Reference request for supersymmetric localization

I would like to ask for some readable introduction or maybe review of the technique of supersymmetric localization for $\mathcal{N}=1,2$ SUSY theories. I would like a different one than the one people ...
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### Volume factor in Faddeev-Popov quantisation

In Faddeev-Popov quantisation, why does the integral over gauge parameter cancel the volume factor of the gauge group that's in the denominator? In fact, I don't understand where the volume factor ...
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I am trying to obtain the polchinski's equation 4.3.16 which is following $Q_B^2 = \frac{1}{2}\{ Q_B, Q_B \} = -\frac{1}{2}g^{K}_{IJ}g^{M}_{KL}c^Ic^Jc^L b_M =0$ Where $Q_B = C^I(G_I^m +\frac{1}{... 1answer 388 views ### Noether Current when the Lagrangian depends on second derivative of the fields Let a Lagrangian density for a field theory of$N$fields$\left\{\phi_i\right\}_{i=1}^N$be given. Assume that the Lagrangian density depends on the fields, their spacetime derivatives, and their ... 1answer 335 views ### Lagrangian depends on second derivative of field In case of the gauge-fixed Faddeev-Popov Lagrangian: $$\mathcal{L}=-\frac{1}{4}F_{\mu\nu}\,^{a}F^{\mu\nu a}+\bar{\psi}\left(i\gamma^{\mu}D_{\mu}-m\right)\psi-\frac{\xi}{2}B^{a}B^{a}+B^{a}\partial^{\... 1answer 162 views ### Yang-Mills Lagrangian invariant under BRST In equation 16.47 in Peskin & Schroeder, it is claimed that$$ -\frac{1}{2}g^2f^{abc}f^{cde}\left(A_{\mu}\,^{b}c^{d}c^{e}+A_{\mu}\,^{d}c^{e}c^{b}+A_{\mu}\,^{e}c^{b}c^{d}\right) ~=~ 0 \tag{16.47}$$... 0answers 84 views ### Old covariant quantization of open string at level N=1 I have a question regarding an equation in Polchinski's "String Theory, Volume 1, An introduction to the bosonic string". The equation is (4.3.27) on p.135. This section is about the brst-cohomology ... 1answer 178 views ### Does the LSZ reduction method prove gauge-independence in massless gauge theories? I've been working my way through L. Baulieu's excellent paper [Perturbative gauge theories, Physics Reports, Volume 129, Issue 1, December 1985, Pages 1-74]. Towards the end, he goes on to prove that ... 1answer 420 views ### The BRST construction for YM with or without auxiliary field I'm learning BRST symmetry for Yang-Mills theory and I see that there are two ways of writing BRST differential. In some books (for example Ryder's and Ramond's textbooks) BRST differential acts as \... 1answer 284 views ### Adding stuff to the path integral (Faddeev-Popov method) I'm wondering about the Faddeev-Popov method described in Peskin Schroeder and also on page 7 in this link. What gives them the right to simply add the Gaussian \omega and thus introduce the \xi ... 0answers 55 views ### A question about the constraints in BRST-Fock theories In BRST Symmetry in the Classical and Quantum Theories of Gauge Systems, Henneaux says the Fock representation is not applicable to an odd number of constraints. Then he goes on to say that the Kugo-... 1answer 332 views ### Gupta-Bleuler Formalism In the Gupta-Bleuler formalism we have a problem with two states (scalar photons and longitudinal photons), because here \langle \vec{k}_a|\vec{k}_b\rangle is negative or zero. However, I thought ... 1answer 349 views ### Ghost fields in particle physics In my particle physics lecture, ghost fields were briefly mentioned. As far as I understand, these come up when computing cross sections by the path integral method, to compensate for equivalent ... 1answer 202 views ### Lorenz gauge in the Gupta-Bleuler Method Greiner in his book Field Quantization page 180 & 181 wrote: As shown in (7.24) the Lorenz condition cannot be enforced as an operator identity. Instead we will use it as a condition for the ... 1answer 87 views ### Ghosts on Torus worldsheet Why after the expansion, only 0-mode of bc-ghost contributes to the 4-points ghost function on a torus worldsheet?$$<c(z_1)b(z_2)\tilde{c}(\bar{z}_3)\tilde{b}(\bar{z}_4)>_{T^2} ~\... 2answers 294 views ### For the$U(1)$problem, is the Kugo and Ojima Goldstone quartet wrong? On page 96 in "Local Covariant Operator Formalism of Non-Abelian Gauge Theories and Quark Confinement Problem", Prog. Theor. Phys. Suppl. 66 (1979) 1, KO state the following: Finally we should ... 1answer 236 views ### Ghost Number Conservation I've been reading about gauge theory quantization, and understand it mostly. The only thing I don't get is why people talk about "ghost number conservation". As far as I can tell, the ghost number is ... 1answer 387 views ### Conservation of BRST current in QED I am trying to understand the conservation of the BRST current in QED but am having some trouble. This is what I have so far, QED lagrangian density in Lorenz gauge is, $$L = \frac{1}{4}F_{\mu\nu}F^{\... 1answer 216 views ### A question about BRST current in bosonic string theory I have a question about Eq. (4.3.3) in Polchinski's string theory book volume I, p. 131. It is said Replacing the X^{\mu} with a general matter CFT, the BRST transformation of the matter fields ... 1answer 120 views ### A question of BRST symmetry of bosonic string theory This question relates to this post I tried to verify Eq. (4.2.7) in Polchinski's string theory book vol I p. 127 but I miserably miss a sign$$ \delta_B (b_A F^A) = i \epsilon (S_2 + S_3) \tag{4.... 1answer 141 views ### How do I show the existence of a conserved ghost number with BRST in bosonic string theory? I have three questions about the BRST symmetry in Polchinski's string theory vol I p. 126-127, which happen together Given a path integral $$\int [ d\phi_i dB_A db_A d c^{\alpha}] \exp(-S_1-S_2-S_3)... 0answers 175 views ### The Integral Trick and An Equality in Nakajima's Lecture In Nekrasov et al's series papers MNS, they calculate such kinds of integral$$ \frac{E_1 E_2}{N(2\pi i)^N(E_1+E_2) }\oint d\phi_1 \wedge d\phi_2\wedge \ldots\wedge d\phi_N \prod_{i<N} (-\phi_i) \... 2answers 181 views ### BRST transformation of adjoint spinor in Yang-Mills-Theory with matter fields a dirac spinor$\psi$transforms under BRST as $$\psi \to \delta_\Omega\psi=i\eta\psi$$ with$\eta$being a ghost field. If I want to get the transformation of ... 1answer 645 views ### How to get the$i\epsilon$prescription for a Faddeev-Popov ghost propagator? In path integral formalism, for a physical field there will be an$i\epsilon$term in the action, which comes from identifying the in and out vacuum, and in turn this$i\epsilon$will naturally appear ... 1answer 238 views ### Quantum master equation in the Batalin-Vilkovisky formalism I am reading the Section 15.9 of Weinberg's book "The Quantum Theory of Fields, vol. 2". Under a shift$\delta\Psi[\chi]$in$\Psi[\chi]$, we have $$\begin{split} \delta Z&=i\int[d\chi]\... 0answers 184 views ### What is the fundamental difference between ghost and auxiliary fields? I am somehow confused by the notion of auxiliary fields, such as for example the fields F and D which appear in supersymmetry, and the notion of ghost fields which appear for example in the BRST ... 0answers 452 views ### Noether currents for the BRST tranformation of Yang-Mills fields The Lagrangian of the Yang-Mills fields is given by$$ \mathcal{L}=-\frac{1}{4}(F^a_{\mu\nu})^2+\bar{\psi}(i\gamma^{\mu} D_{\mu}-m)\psi-\frac{1}{2\xi}(\partial\cdot A^a)^2+ \bar{c}^a(\partial\... 1answer 138 views ### Negative open string norms after BRST cohomology? The question Disappearance of moduli for condensate of open strings made me think. Suppose we have a Dp-brane completely wrapped over a$T^d$compactification with$p\leqslant d$. Look at an open ... 2answers 540 views ### Kugo and Ojima's Canonical Formulation of Yang-Mills using BRST I am trying to study the canonical formulation of Yang-Mills theories so that I have direct access to the$n$-particle of the theory (i.e. the Hilbert Space). To that end, I am following Kugo and ... 3answers 209 views ### Quantizing first-class constraints for open algebras: can Hermiticity and noncommutativity coexist? An open algebra for a collection of first-class constraints,$G_a$,$a=1,\cdots, r$, is given by the Poisson bracket$\{ G_a, G_b \} = {f_{ab}}^c[\phi] G_c$classically, where the structure constants ... 1answer 646 views ### Clarification on “central charge equals number of degrees of freedom” It's often stated that the central charge c of a CFT counts the degrees of freedom: it adds up when stacking different fields, decreases as you integrate out UV dof from one fixed point to another, ... 3answers 199 views ### Is BRST ghost number conserved in quantum gravity? Quantum gravity needs Faddeev-Popov ghosts. Feynman showed that. Take a black hole. Hawking pair production of ghost-antighost pair. One ghost falls into the hole and hits the singularity. The ghost ... 2answers 583 views ### What is the ontological status of Faddeev Popov ghosts? We all know Faddeev-Popov ghosts are needed in manifestly Lorentz covariant nonabelian quantum gauge theories. We also all know they decouple from the rest of matter asymptotically, although they "... 1answer 168 views ### Request for Reference: BRST formalism/transformations Could anyone please suggest a very basic paper/reference/literature on BRST symmetry/formalism that requires rudimentary knowledge of Dirac's method for dealing with constrained systems and generation ... 1answer 307 views ### Who added$\frac{3}{2} \partial^2 c\$ to the virasoro BRST current (and why)?

I've been looking at the literature on quantizing the bosonic string, and I noticed that there was a change made in the definition of the BRST current around 1992. However, I haven't found any ...
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### Virasoro constraints in quantization of the Polyakov action

The generators of the Virasoro algebra (actually two copies thereof) appear as constraints in the classical theory of the Polyakov action (after gauge fixing). However, when quantizing only "half" of ...