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.

Quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics and is used to construct physical models of subatomic particles in particle physics/high-energy physics, quasiparticles in condensed matter physics and highly relevant to statistical field theory.

QFT treats particles as excited states (also called quanta) of their underlying fields, which are — in a sense—more fundamental than the basic particles. Interactions between particles are described by interaction terms in the Lagrangian involving their corresponding fields. Each interaction can be visually represented by Feynman diagrams, which are formal computational tools, in the process of relativistic perturbation theory.

433 questions
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Proving gauge invariance using the Schwinger-Dyson equation

The problem is as follows: Consider a quantum field theory on a Lorentzian four-dimensional spacetime $(M,g)$ with action $S[\phi]$. Let $\mathcal{A}$ be the algebra of observables of the theory, and let $\mathcal{H}$ be the Hilbert space of the…
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About sending time to infinity in a slightly imaginary direction in QFT

I am going through the Peskin and Schroeder QFT book. While proving the Gell-Mann and Low theorem in chapter 4 of their book, the authors started with the equation \begin{equation} e^{-iHt}|0\rangle = e^{-iE_{0}t}| \Omega\rangle \langle \Omega | 0…
Mass
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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 transformation. The relevant portion is in this…
samgon
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Represent a square-root of determinant by Grassmann numbers

I am thinking about the representation of $ \sqrt{\det A}$ for a Matrix $A$ . Since it is known that for the Grassmann numbers $ \eta, \eta ' $ the following relation holds: $$ \int \int d \eta d \eta' \exp\left[\eta'^T A \eta\right] = \det…
kryomaxim
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Invariance of Lagrangian density under gauge transformation

In a problem in my QFT course i am asked to write down the most general posible Lorentz invarient Lagrangian density for a vector field (at most quadratic in the field and in the derivatives) and to find what it reduces to if we ask for gauge…
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Understanding the operators required to derive a more generalised form of the Schrodinger equation.

The following is an excerpt from my lecture notes, aiming to derive a more general form of the Schrodinger equation. There has been little reason for the introduction of the commutation relations given in (3.3) regarding the operators…
user955291
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What are some of the prerequisites for studying quantum field theory?

What are the mathematical and physics prerequisites for studying quantum field theory?
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Quantum field theory, interpretation of commutation relation

Let $\phi$ be the quantum field $$ \phi(x) = \int \frac{d^3\mathbf{p}}{(2\pi)^3} \frac{1}{\sqrt{2E_\mathbf{p}}} \Big[ b_\mathbf{p}e^{-ip\cdot x} + c_\mathbf{p}^\dagger e^{ip\cdot x} \Big] $$ with commutation relations $$ [b_\mathbf{p},…
Bernoulli
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Computing energy-momentum tensor with arrowed Feynman slash derivative

Given a four component Dirac spinor $\psi$ (working classically) and the usual Dirac matrices $\gamma^{\mu}$, one can construct a Lagrangian $$\mathcal{L} = \bar{\psi}(i\overset{\leftrightarrow}{{\not\partial}} - m)\psi =…
FH93
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