# 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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### According to Hartle-Hawking state, could we build a sum over all possible metrics (including non-compact ones)?

Physicists Stephen W Hawking and James B Hartle 1 proposed that the universe, in its origins, had no boundary conditions both in space and time. To do that, they proposed a sum over all compact ...
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### Expression for sum over paths

In an introductory lecture on the path integral formalism, I came across the following. Suppose that $\gamma$'s are paths such that a particle travelling along any of them reaches the position co-...
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### Symmetries in quantum field theory and anomalies

Suppose we have a lagrangian quantum field theory, thus a theory where we can write an action in the form \begin{equation} S = \displaystyle \int d^4 x \; \mathcal L \, \left( \partial_{\mu} \phi , \...
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### Scalar field propagator in curved space from path integral

Consider a scalar masless field (in 2d for concreteness) in a curved space with standard action $$S=\frac{1}{4\pi}\int d^2x \sqrt{g}g^{ab}\nabla_a\phi\nabla_b \phi$$ There is an elegant way to derive ...
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### Integrating out massive degrees of freedom of Super Yang-Mills Action in Matrix Theory

From this paper, I want to integrate out the massive degrees of freedom. The total action $S$ is given by $$S = S_{Y} + S_{A} + S_{Fermi} + S_{ghost}$$ where the terms are given in equations (2.9),(...
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### Decoupling of ghost fields in axial-gauge QCD

After quantizing QCD using the Faddeev-Popov "prescription", we end up with the original QCD Lagrangian plus the gauge-fixing term, \begin{equation} -\frac{1}{2\alpha}(n\cdot A)^2, \end{equation} and ...
### Supersymmetric localisation of 2D super YM on $S^2$
In QM using Feynman path integral(FPI) we derive the propagator of free particle which comes out to $$(f(t))e^{iS_{cl}/\hbar}$$ But in QFT the Feynman propagator is derived using the differential ...