# Questions tagged [path-integral]

Path integral formulation (Due to Feynman) is a major formulation of Quantum Mechanics along with Matrix mechanics (Due to Heisenberg and Pauli), Wave Mechanics (Due to Schrodinger), and Variational Mechanics (Due to Dirac). DO NOT USE THIS TAG for line/contour integrals.

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### $S$-matrix elements in path integral approach

How to calculate $S$-matrix elements of quantum electrodynamics using path integral formalism?
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### Infrared regularizing the harmonic oscillator path integral

This is from Laine and Vuorinen’s Basics of Thermal Field Theory. I do not understand why the fact that the integral over $x(\tau)$ implies the following regularization scheme. That is, I don’t ...
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### How does path integral quantization ensure unitarity?

Unitarity can be verified post hoc by examining the optical theorem. In the context of path integral quantization where formal derivation starting from canonical quantization is unavailable, is it ...
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### Reference request for semiclassical approximations for Schwinger-Keldysh path integrals

Can some one provide some resources for understanding semi-classical approximations for Schwinger-Keldysh path integrals. Is there any discussion about instanton (and multi-instanton) (for even single ...
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### Gaussian Grassmann integral with complex/bosonic source term

I'm interested in solving the following multi-dimensional integral $$\int d \theta d \bar{\theta} e^{-\bar{\theta}M \theta +\Lambda \theta + \bar{\theta} J }$$ where $\theta$ is a $N$-dimensional ...
254 views

### Question on Majorana Path Integral

I'm studying Shankar's Quantum Field Theory and Condensed Matter and got stuck in the issue related to changing measure in Majorana path integral. In section 9.4, the Euclidean action for the ...
333 views

### Discretized derivation of Majorana path integral

Shankar's QFT book gives an overview for deriving a path integral representation for Majorana fermions. In the derivation, he works directly in continuous imaginary time, sweeping issues of ...
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### Fermion Determinant [closed]

When we calculate fermion determinant for either Majorana or Weyl spinors, why do we get an extra factor of half in the coefficient of the determinant as compared to the Ghost determinant?
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### How important are purely imaginary finite action solutions for first-order instanton contributions?

I am working on a physics problem where I have to calculate instanton contributions for a non-relativistic Hamiltonian $$H=-\frac{1}{2}\frac{d^2}{dx^2}+\frac{1}{2}x^2+\frac{1}{6}g^2x^6 \tag 1$$ for ...
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### Fourier transform of the Gaussian action for the real scalar bosonic field

In my current homework, we have to get familiar with quadratic theory in order to reach $\phi^4$-theory. So the starting point is $$Z = \int Dx e^{-S[\phi]}$$ with the action for the real scalar ...
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### Path integral for complex scalar field

I am taking a QFT course which focuses on the path integral formulation. At a certain point, I was confused because we saw that, when integrating over complex Grassmann fields for fermions, we defined ...
259 views

### Deriving a path-integral expression for a thermal density matrix with position-dependent temperature

I've been fiddling with deriving a path-integral expression for a thermal partition function with a position-dependent temperature but I'm not sure how to get started on this. Concretely, I'm trying ...
327 views

### Correct method for splitting path integral in two

In 3D point particle quantum mechanics we have that the propagator can be represented as a path integral \langle x|e^{-iHt}|y\rangle =\int_{\gamma(0)=x}^{\gamma(t)=y}\mathcal{D}[\...
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### How to derive the gauge invariance of Yang-Mills action with external source?

In the Faddeev-Popov procedure of path integral of $$Z[J] = \int [DA] e^{iS(A,J)}, \quad S(A,J)= \int d^4x [-\frac{1}{4}F^{a\mu\nu}F_{a\mu\nu} + J^{a\mu}A_{a\mu} ]$$ we have used that $S(A,J)$ is ...
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### Does a quantum field theory have an effective single-particle action in the single-particle subspace?

In non-interacting quantum field theories, the particle number is conserved so we can restrict to a given subspace of fixed particle number. On the single-particle subspace, the state will evolve ...
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### What happens to branching in the Many-Worlds Interpretation of quantum mechanics in the limit when Planck's constant goes to 0?

We learn from quantum mechanics courses that one recovers classical mechanics in the limit when Planck's constant goes to zero. This can be seen in the path integral formulation. This is why ...
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### In QFT when performing path integral, why don’t we divide it by the volume of Poincaré group, as what we did for gauge group?

When performing path integral in gauge theory, we naively want to compute $$Z = \int DA \exp(iS[A])$$ But we noticed, that because the action is the same for gauge equivalent conditions, we should ...
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### Euclidean functional Integrals: Existence of zero eigenvalue due to time translation symmetry

In the chapter "Uses of Instantons" from the book "aspects of symmetry" by Sidney Coleman I have come across the euclidean version of the path integral in semi-classical ...
1 vote
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### What is the gravitational path integral computing?

What is the gravitational path integral (which roughly goes like $\int [dg]e^{iS_{\text{EH}}[g]}$) computing? Usually, path integrals arise from transition amplitudes such as these: \$\lim_{T\to\infty}\...
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### On Gravity and the Path Integral

The path integral, in the simplest case, usually attributes a classical action to every conceivable trajectory a particle can take between to points in spacetime. This assumes a flat, Minkowski ...