# Questions tagged [quantum-field-theory]

Use this tag for questions about quantum field theory in theoretical/mathematical physics. Quantum Field Theory is the theoretical framework describing the quantization of classical fields allowing a Lorentz-invariant formulation of quantum mechanics. Associate with [tag:mathematical-physics] if necessary.

244 questions
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### Rewriting a state as a field in CFT

I've been working through a textbook and course on conformal field theory recently. However in a section illustrating how to calculate correlators for secondary fields (using the free boson as an ...
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### Proving a state is a KMS state

Define an *-algebra generated by the symbols $W(u)$ for $u\in \mathbb{C}$ subject to the relation $$W(u)W(v) := e^{\frac{1}{2}i\Im(\overline{v}u)}W(u+v), W(u)^* = W(-u)\quad u,v \in \mathbb{C}.$$ ...
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### Proofing equation containing time-ordering operator

Preparing for a presentation at university (I'm a Bachelor physics student) I have come across the formula below containg the time-ordering operator $T$. Although i have now understood the action of ...
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### Navier-Stokes smoothness problem and Gauge Theory

Recently, I came across this paper where the author describes an analogy between electrodynamics and fluid dynamics. He develops a one-to-one correspondence between the equations of electrodynamics ...
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### Rigorous proof of quantum electrodynamics renormalization

In most physics books they give proofs of renormalization of quantum electrodynamics that are not mathematically rigorous. Is there any book or article that give a formal proof of quantum ...
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### Solving an integral related to QFT, using identity 3.914 from Gradshteyn-Ryzhik

Given the following formula (#3.914, Gradshteyn-Ryzhik,1980): \begin{equation} \displaystyle\int\limits_0^\infty e^{-\beta{\sqrt{\gamma^2+x^2}}}\cos(bx)dx=\frac{\beta\gamma}{\sqrt{\beta^2+b^2}}K_1(\...
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### Question on Turaev's paper about axioms for topological quantum field theory

I am currently reading Turaev's paper Axioms for topological quantum field theory. In couple of place, there is a paraphrase "... is natural with respect to $\mathfrak{U}$-homeomorphism" and I don'...
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### Is the comparator $U(y,x)$ in Gauge Theory the same as a holonomy?

For Gauge theories you have a comparator that transforms as $$U(y,x) = e^{i\alpha(y)}U(y,x) e^{-i\alpha(x)}$$ Is this the same thing as the holonomy?
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### Delta/metric question (context commutator poincare transf.)

The problem statement, all variables and given/known data Relevant equations I believe that $\frac{\partial x^u}{\partial x^p} =\delta ^u_p$ (1) $\implies$ (if $\delta^a_b$ is a tensor, I'm not ...
1answer
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### Functional derivative in QFT

Introductory overview I have that $$iW_0[J] := -\frac{1}{2}\int d^4x d^4 y J(x)D_F(x-y)J(y)$$ and I'm trying to perform the calculation of a two-point function $G^{(2)}(x,y)$ from the fully ...
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### Does the singularities of black holes not being simply connected imply that the universal coverings of quantum field theory fail?

Does the singularities of black holes not being simply connected imply that the universal coverings of the usual types of Lie groups of quantum field theory fail? I was downvoted and told that I need ...
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### QFT, Noether and Invariance, Complex fields, Equal mass

The problem statement, all variables and given/known data Question attached: Hi I am pretty stuck on part d. I've broken the fields into real and imaginary parts as asked to and tried to compare ...
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### Yang–Mills theory and mass gap

I am interested in widening my knowledge into the formal aspects of Yang–Mills theory. In particular, I would like to study the current mathematical and physical research literature about this ...
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### Conserved currents under Lorentz Transformations

I'm reading David Tong's notes on quantum field theory, and I had a question from page 17 (equations 1.54-55), where he is deriving the conserved currents that arise from a symmetry under a Lorentz ...