# Tagged Questions

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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### What is a path integral? [closed]

I was reading about path integrals because someone told me about it in this question. I read some articles about path integrals but couldn't understand it. Can you please explain path integral for me? ...
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### Least Action Principle (Classical and Quantum Theory)

I) My first question would be "why should classical systems obey the principle of least action ?" When we find out the propagator in quantum physics, we find the amplitude to be equal to the sum over ...
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### What makes Lattice Yang-Mills hard?

I've been reading up on non-perturbative Yang-Mills, and have found the following equation: $$Z[\gamma, g^2, G]=\int \! \prod e^{-S}\mathrm{d}U_i$$ Now I don't know much about computational physics, ...
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### Why every state evolving infinite time becomes the ground state in QFT?

For any state $|\phi \rangle$ evolving infinite time $$\lim\limits_{t\rightarrow \infty} e^{-iHt}|\phi\rangle=\lim\limits_{t\rightarrow \infty} e^{-iHt}|n\rangle\langle n|\phi\rangle$$ Let ...
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The generating functional for a free Dirac field is $$Z_0[\eta,\bar{\eta}]=\int D\bar{\psi}D\psi \mathrm{exp}\{i\int [\bar{\psi}(x)S^{-1}\psi(x)+\bar{\eta}(x)\psi(x)+\bar{\psi}(x)\eta(x)]dx\}$$ where ...
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### Heterotic Supersymmetric derivation of an integrality theorem for differentiable manifolds [closed]

Please consider the following integrality theorem for differentiable manifolds due to K H Mayer: I am trying to prove this theorem using Heterotic Super-symmetric Quantum Mechanics described by a ...
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### Why isn't the path integral defined for non homotopic paths?

Context In the Aharonov Bohm effect, there is a solenoid which creates a magnetic field. Since the electron cannot be inside the solenoid, the configuration space is not simply connected. Question ...
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### What's the importance of background field gauge?

Recently I've read that background field gauge is very convenient for gauge theories, because it fixes the connection between normalization constants of gauge field and gauge coupling constant one. I ...
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### Vacuum to vacuum transition amplitude using functional integral

The vacuum to vacuum transition amplitude for a free particle with source $J$ is given by $$Z_0[J]=\int D\phi \mathrm{exp}\{-i\int [\frac{1}{2}\phi(\square +m^2-i\epsilon)\phi-\phi J]d^4x\}$$ Let ...
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### How does path integral formulation explain bound states?

It seems to me that the intuitive explanation of path integrals in quantum mechanics describes scattering processes only. You have a particle going from A to B and you compute the probability ...
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### Renormalization, integrating out high momenta Wilson way

In equation $(12.5)$ in Peskin and Schroeder, they write out the generating function but leave out all quadratic terms of the form $\phi\hat{\phi}$ arguing that they vanish since Fourier ...
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### Semiclassical limit of Quantum Mechanics

I find myself often puzzled with the different definitions one gives to "semiclassical limits" in the context of quantum mechanics, in other words limits that eventually turn quantum mechanics into ...
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### Can the diffraction/interference pattern behind the slit (double slit) be calculated with Feynman path integrals (QED)?

I often see Feynman path integrals explained by a graphic which shows the slit and then the electron goes all possible ways behind the slit. Ok that is nice to understand the Feynman path integral, ...
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### Bound states and extensive field configurations

What are extensive field configurations in QFT (instantons, monopoles etc.)? What is the difference in description of their contribution in path integral value or in $n$-point operator functions ...
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### Question about the foundation of part I in A. Zee's book

Zee says in Section I.3 of QFT in a nutshell: The functional integral $$Z = \int D \varphi e^{i \int d^4 x [\frac{1}{2} (\partial \varphi)^2 - V(\varphi) + J(x) \varphi (x)]} \tag{11}$$ is ...
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I would like to derive the partition function for the quantum Harmonic oscillator from scratch: $$\tag{1} Z = \int dp \, dx\, e^{-\beta H}.$$ The free particle appears in many textbooks. $H = ... 1answer 132 views ### Where does this delta of zero come from? It is common when evaluating the partition function for a$O(N)$non-linear sigma model to enforce the confinement to the$N\$-sphere with a delta functional, so that $$Z ~=~ \int d[\pi] d[\sigma] ~ ... 4answers 1k views ### In which field of mathematics do I learn path integrals? I don't mean line integrals, I am talking about path integrals or functional integrals like the ones that Feynman introduced to quantum mechanics. And what are the prerequisites to this field of ... 1answer 418 views ### Free Particle Path Integral Matsubara Frequency I am trying to calculate$$Z = \int\limits_{\phi(\beta) = \phi(0) =0} D \phi\ e^{-\frac{1}{2} \int_0^{\beta} d\tau \dot{\phi}^2}$$without transforming it to the Matsubara frequency space, I can ... 1answer 404 views ### Matsubara Frequencies [closed] I have to evaluate the following Matsubara sum:$$\frac1\beta \sum \left(\omega^2 +a^2\right)^{-1}$$for Bosonic-Matsubara frequencies. I know contour integration it the way to go. Therefore, I ... 0answers 97 views ### Proximity effect and integrating out the quasiparticle degrees of freedom I am reading at the moment the paper http://arxiv.org/abs/1401.5203 and try to reproduce the results. One result is the proximity correction S_{\Sigma} to the system$$ e^{-S_{\Sigma}} ...
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Suppose I have some Lagrangian of some higher derivative gravity coupled to a may be matter fields. Now I want to fluctuate it to quadratic order about an AdS background and calculate the 1-loop ...
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### Relationship between the Black-Scholes model and path integrals

This question was inspired by some interesting comments by Rod Vance on this answer. Could you (Rod), or someone else, expand on these comments and give a brief summary of the connection between the ...