# 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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### How to verify this statement in optical theorem?

There is a statement in optical theorem (From Peskin & Schroeder): It is easily checked (in QED, for example) that each diagram contributing to an S-matrix element $\mathcal{M}$ is purely real ...
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### What's the path of least action for fermions off-shell?

The Lagrangian of fermions is first order both in space-derivatives and time-derivatives. In the variation of the action one usually fixes both the initial point and end point. I have the following ...
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### Supersymmetric localisation of 2D super YM on $S^2$

I wanna to understand how to calculate partition function for pure abelian Yang-Mills theory. To do this, I need follow some usual step's (I follow Benini, Localization in supersymmetric field ...
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### Is there a deep reason why action comes from a local lagrangian?

In both classical and quantum physics Lagrangians play a very important role. In classical physics, paths that extremize the action $S$ are the solutions of the Euler-Lagrange equations, and the ...
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### Is the Feynman's path integral a density?

The Feynman-Kac path integral formula is used to solve parabolic equations related to stochastic processes. Considering the probabilistic expression, the solution is indeed not a density. However, ...
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### How to connect Green function to propagator?

I know that there has already been many questions related to this question, such as in Differentiating Propagator, Green's function, Correlation function, etc. However, that question mainly ...
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### Can the real-time Green's function be written in the form of path integral on the real axis?

In every textbook, the path integral of the Green's function is written in imaginary-time. I wonder whether we could write real-time green function in the path integral form.
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### Fourier transform of matrix element of evolution operator

I learn ''Path integrals in quantum mechanics'' by Jean Zinn-Justin now. There is a chapter about calculating the path integral for particle on a ring (rigid rotator). So, after some calculations we ...
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### Normalizing Propagators (Path Integrals)

In the context of quantum mechanics via path integrals the normalization of the propagator as $$\left | \int d x K(x,t;x_0,t_0) \right |^2 ~=~ 1$$ is incorrect. But why? It gives the correct pre-...
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### Integrating the gauge covariant derivative by parts

I was watching a set of lectures on effective field theory and the lecturer said that you can always integrate the covariant derivative by parts due to gauge symmetry. For example, if I understand ...
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### Fixing time in Feynman phase space path integral

The phase space version of Feynman's path integral expression for the free particle propagator involves a (formal) sum over paths in phase space with fixed $q$ endpoints and (as far as I'm aware) ...
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### Self-intersecting paths in Feynman path integral

The self-intersecting paths are not included in the Feynman path integral (FPI) approach because by definition a curve is defined as $\gamma:\mathbb{R}\rightarrow \mathbb{R}^3$ and since we take the ...
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### Relation between Feynman path integral and time ordering operator

Is there any relationship between Feynman path integral approach and time ordering operator because both of the approaches obliterate the idea of noncommutativity of operators since in FPI the ...
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### Which vacuum do I use for the path-integral?

In Weinberg, vol. 1, Section 9.2, Weinberg defines the in and out vacua as states with no particles (9.2.4): $$a_{\rm in}|{\rm VAC,in}\rangle=0$$ $$a_{\rm out}|{\rm VAC,out}\rangle=0$$ He does this ...
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### Coherent state basis of (relativistic) particle Fock space

For a neutral scalar bosonic particle of mass $m$, I consider a Fock space with an orthonormal basis of momenta eigenstates \begin{equation}\label{Fock-p-states} \left|p_1p_2\cdots p_n\right\rangle=\...
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### Do Feynman path integrals satisfy Bell locality assumption?

There are generally two basic ways to solve physics models: Directional, e.g. Euler-Lagrange equation in CM, Schrödinger equation in QM. We evolve some initial conditions in some direction, can ...
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### Clarification regarding animation on path integrals

The wikipedia page on path integrals contains the following animation. It's a pretty animation. Sadly the wiki page only says the following on the animation: The diagram shows the contribution of ...
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### Relation between worldsheets and worldlines

If we want to find the propagator of say a zero-spin particle, the formal inverse can be computed by introducing $$-i\int_{0}^{\infty}e^{i(p^2 - m^2)s}\mathrm{d}s$$ We can rewrite this in path ...
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### Physicist path integral and cylinder set measures

Path integral via discretization So let me start with what seems to be the point of view of physicists (corrections are highly appreciated since this is just what I understood!). Let a quantum system ...
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### Boundary conditions of fermionic coherent states path integral

Given the algebra of a fermionic oscillator $$\{\hat{a},\hat{a}^\dagger \}=1\,, \qquad \hat{a}^2=(\hat{a}^\dagger)^2=0,$$ with coherent states $\hat{a}|\xi\rangle=\xi|\xi\rangle$, let's ...
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### Why can the time-ordered exponentials be brought to the right?

Having worked through almost all calculations in section 4.2 of Peskin & Schroeder's An Introduction to QFT, I still don't get why we can get to Eq. (4.31) \begin{equation} <\Omega|\mathcal{T}\...
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### Boundary conditions in holomorphic/coherent state path integral

Consider the holomorphic representation of the path integral (for a single degree of freedom):  U(a^{*}, a, t'', t') = \int e^{\alpha^{*}(t'') \alpha(t'')} \exp\left\{\intop_{t'}^{t''} dt \left( -a^...
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### Violation of Bell-like inequalities with spatial Boltzmann path ensemble: Ising model?

Quantum mechanics is equivalent with Feynman path ensemble, which after Wick rotation becomes Boltzmann path ensemble, which can be normalized into stochastic process as maximal entropy random walk (...
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### What is the constraint on the Gauge Potential in the Covariant Gauges?

One of the most common gauges in QED computations are the $R_{\xi}$ gauges obtained by adding a term \begin{equation} -\frac{(\partial_\mu A^{\mu})^2}{2\xi} \end{equation} to the Lagrangian. ...
### Calculating $S$-matrix in string theory
To calculate string $S$-matrix, we mainly use Faddeev-Popov gauge fixing method, as in chapter 6 of Polchinsky's book 《string theory》. But in section 6.2, 'tree level amplitude', I didn't find ...