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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24 views

Exchanging a local operator with a path integral

I am reading a paper by J. Polchinski, called "What is string theory", hep-th/9411028. In eq. 1.1.9, and the line before it, the author seems to have used: $$<\partial_z \partial_{\bar{z}} ...
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46 views

Connexion of S matrix and path integral [on hold]

I have been studing the path integral formalism but all I am finding is how to calculate time ordering product. How can we connect it with the S-matrix in the canonical formalism?
3
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1answer
55 views

Propagator from Path integral

In class we have proved something like: $$ \frac{\partial^2 Z(J,\bar{J})}{\partial J(x) \partial \bar{J}(x')}\frac{1}{Z}|_{J=\bar{J}=0}=\Delta(x-x').$$ That by introducing source terms to path ...
2
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0answers
69 views

Analyzing the free-particle kernel [closed]

I recently began studying the theory of path integrals from the book by Feynman and Hibbs. The Problem $3.6$ asks to give an argument to show that $F(t_b,t_a)$ depends only on $t_b-t_a$. ...
2
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0answers
52 views

Determinants in path integrals in gauge theories and geometry

I know that in the formalism of path integral it is easy to show how determinants, corresponding to gauge fixing condition and FP ghosts, appear. But there is strict explanation of these determinants ...
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46 views

Feynman's Path Integral Approach: The Complex Exponentiated Action [duplicate]

I'm working on a project covering Feynman's Path Integral Approach. I'm having trouble intuitively grasping what motivates the introduction of the expression $e^\frac{iS}{\hbar}$, where S is the ...
2
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2answers
52 views

Where is the BRST symmetry?

When quantizing YM we start from the gauge fixed path integral (to remove redundancy of integrating over Gauge symmetric configurations) $$\int \mathcal{D}A \delta(G(A)) \text{det} \Delta_{FP}e^{i\int ...
3
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0answers
33 views

In path integral of multiply connected manifold, how to prove the partial amplitudes are linear independent? [closed]

In path integral of multiply connected manifold $X$, $$K(b,t_b;a,t_a)=\sum_{\alpha\in \pi_{1}}\chi(\alpha)K^{\alpha}(b,t_b;a,t_a)$$ where $K^\alpha$ is called partial amplitude, $\alpha$ denotes the ...
7
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1answer
165 views

What's the Propagator in the Free Particle Case? (Path Integrals with Source Term)

If I take the Lagrangian to be, $$L(t)=\frac{1}{2}m \dot q(t)^2$$ The Euclidean Path Integral is supposed to be, $$K=\int D[q(t)] \ e^{-\int L(\dot q) d \tau}$$ If I add a source term $J(\tau)$ we ...
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0answers
64 views

Path integral (sum over paths where $v>c$) [closed]

The path integral formalism is used to get for example the propagator of particles. In this formalism we integrate over all mathematically possible paths (and weight them with the non-relativistic ...
4
votes
2answers
119 views

Are the path integral formalism and the operator formalism inequivalent?

Abstract The definition of the propagator $\Delta(x)$ in the path integral formalism (PI) is different from the definition in the operator formalism (OF). In general the definitions agree, but it is ...
6
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0answers
70 views

Is it possible to do a path integral between two boundaries analytically on a quantum lattice?

I have been trying to perform some path integral between two boundaries for a massless scalar field $$\int_{\varphi(t_a, \vec{x})}^{\varphi(t_b, \vec{x})} \mathcal{D}\varphi(x)e^{iS[\varphi(x)]}$$ ...
3
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0answers
41 views

Linear Response And path integral

I'm following Wen's book on Quantum field theory, and I'm struggling with section 2.2.1 on linear response and response functions. Specifically I'm unable to reproduce equation 2.2.7 in which the ...
4
votes
2answers
314 views

Physical meaning of partition function in QFT

When we have the generating functional $Z$ for a scalar field \begin{equation} Z(J,J^{\dagger}) = \int{D\phi^{\dagger}D\phi \; \exp\Big[{\int L+\phi^{\dagger}J(x)+J^{\dagger}(x)}\phi\Big]}, ...
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0answers
29 views

Estimation of an Entropic Path Integral

I'm trying to reproduce some results from a paper (http://www.alexwg.org/publications/PhysRevLett_110-168702.pdf for reference) and basically I need a way of estimating a particular path integral ...
8
votes
2answers
195 views

Itô or Stratonovich calculus: which one is more relevant from the point of view of physics?

Langevin equation provides an example of a physical model which involves a differential equation with a stochastic term. Now, I wonder, how should one treat this? When I studied stochastic processes, ...
4
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2answers
90 views

Path Integral Quantization in General Relativity

In Ref. 1 I have seen that the action must contain only the first derivative of the metric as required by the path integral approach. I don't understand why. I mean why the path integral approach of ...
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0answers
30 views

The central limit theorem from a path integral?

On https://en.wikipedia.org/wiki/Path_integral_formulation it is noted that the central limit theorem can be interpreted as the first historical evaluation of a statistical path integral. Is this ...
1
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1answer
51 views

Addtional QFT Book synergetic to Srednicki. Differences $\phi^4$ and $\phi^3$ [duplicate]

I currently hear a course to basic QFT in path integral formulation. Focus is on few and elementary particles, not on many body systems. The lecturer follows the book of Srednicki, which therefore ...
1
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2answers
57 views

Feynman path integral course online [duplicate]

There are a lot of books dealing with Feynman path integrals. Are there any online courses introducing Feynman path integrals and their applications?
6
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1answer
108 views

Are path integrals integrals with countable or uncountable infinite dimensions?

Path integrals are integrals with infinite dimensions. But I recently became confused about if the number of dimensions are discrete/countable or continuous/uncountable. I always thought it should be ...
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0answers
54 views

How to get anti-commuting rule from the view of field?

I was reading the 1951 Lectures on Advanced Quantum Mechanics and I found something really disturbing. That's the anti-commuting rule mentioned on Page 40 at last. Though it was named as Quantum ...
2
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1answer
94 views

Geometric derivation of quantum mechanics from Lagrangian mechanics

I have used classical Lagrangian mechanics for quite a while, and what I like about it is that everything can be derived from a very small number of geometric principles. There are just three things ...
0
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1answer
82 views

General properties of Matsubara frequency summations

By properties such as linearity, shifting, commutativity, etc. I was hoping to evaluate something like, $$S_\eta = \dfrac{1}{\beta}\displaystyle\sum_{i\omega} ...
0
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1answer
14 views

Motivation for integrals over scalar field

I'm looking for good examples of physical motivation for integrals over scalar field. Here is an example I've seen: If you want to know the final temperature of an object that travels through a ...
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2answers
92 views

Zeta regularization of Infinite product

I was trying to compute the product $$ P_{a,b} = \prod_{n=1}^\infty(an + b), $$ after I computed $$ P_{1,b} = \prod_{n=1}^\infty(n + b) = \frac{\sqrt{2\pi}}{\Gamma(b+1)}, $$ and the well-known ...
3
votes
1answer
90 views

Evaluating path integral

I am having some trouble remembering how to evaluate path integrals involving multiple particles. Suppose that I have two interacting particles with Lagrangian $$L= \frac{1}{2}m \dot y^2-\frac{1}{2}m ...
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0answers
33 views

free energy in the path integral equivalent to the classical 1D Ising model: Shankar

In chapter 21 (eqtn 21.2.90) Shankar gives the free energy (of the PI problem equivalent to the classical 1D Ising model), $$ f=-E_0 = K^* $$ I dont understand how he arrives at this considering in ...
4
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2answers
96 views

Anomalous Slavnov-Taylor identity

I will be happy if someone could clarify the mystery here. Consider the following derivation of the anomalous Slavnov-Identity. It's based on lecture notes by Adel Bilal. Suppose we have an action ...
8
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2answers
183 views

Quantum Anomalies and Quantum Symmetries

In Quantum Field Theories (QFT) there is a well known phenomenon of anomalies, where a classical symmetry is broken in the quantum theory due to a so called anomaly. This symmetry breaking can be ...
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0answers
51 views

Chern Simons Theory over S^3 as integral - what is domain of integration?

I found these nice lecture notes Lectures on localization and matrix models in supersymmetric Chern-Simons-matter theories so I am hoping to understand some parts of the Chern Simons theory better. ...
0
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1answer
73 views

Coherent state path integral - derivation

I divided the time interval $[t_0=:t_i,t_f:=t_N]$ into $N$ steps $[t_{k-1},t_{k}],\, k=1,\dots, N$ and applied the resolution of unity for coherent states \begin{equation} ...
3
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1answer
100 views

Free space propagator: reconciling two results

In quantum mechanics, the free space propagator $G(q_f=0,q_i=0;\tau)$ can be easily calculated to be $$\sqrt{\frac{m}{2\pi i \hbar \tau}}$$ by inserting an identity operator. However if we use ...
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0answers
70 views

Making mathematical sense on a Feynman's path integral equation

Usually we find this relation in the context of Feynman's path integral (see, for example, Maggiore's book on QFT, pg 223): $ \int_{q_i}^{q_f}[dq] = \int_{-\infty}^{\infty}d\bar{q}\int_{q_i}^{\bar ...
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0answers
54 views

How does satisfying the Euler-Lagrange equation put a Classical Path on-shell?

I am thinking of what the Euler-Lagrange equation, $$ \frac{d}{dt}\left(\frac{\partial L}{\partial \dot{x}}\right) - \frac{\partial L}{\partial x} = 0 $$ specifically represents in satisfying the ...
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0answers
45 views

Path Integral Formulation [duplicate]

The contribution to the propagator from a particular trajectory is $e^{\frac{iS[x(t)]}{ћ}}$. Does anyone knows how to get to this $e^{\frac{iS[x(t)]}{ћ}}$? As in showing me any reliable source ...
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48 views

Is the Symmetry factor different in Path integral Formalism?

Is the Symmetry factor different in Path integral Formalism and the Perturbation theory (canonical) formalism? For example, the order-1 4-point cross X diagram in the $\phi^4$ theory has symmetry ...
3
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2answers
114 views

Principle of least action: $\frac{d S_{cl}}{dt_b} = \frac{\partial S_{cl}}{\partial t_b} + \frac{\partial S_{cl}}{\partial x_b}\dot{x}_b$

Question I cannot see how I can obtain the yellow highlighted section on the RHS from that of the LHS. The following equation can be found in both my lecture notes(*1) (page 9, equation 2.7) and is ...
1
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1answer
52 views

Feynman Path Integral as a Quantization Scheme

Why isn't the path integral usually discussed as a quantization scheme, like geometric and deformation quantization? Was searching wikipedia for this.
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4answers
182 views

Is the Path Integral formulation of QM just a mathematical tool? [closed]

Is the Path Integral formulation of QM just a mathematical tool or does it offer deep physical insights on the nature of QM? Is it just an alternate way to describe Quantum Mechanics? Could someone ...
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0answers
87 views

Unsolved Potentials in Path Integral

I just started learning on path integral on my own. It seems that the path integral method is not always able to be solved, depending on the potential. On the other hand, these potentials are ...
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0answers
75 views

Transition Amplitude in Field Theory

I am currently reading the "Quantum Field Theory" by Lewis Ryder. In chapter 5 he is talking about path integrals and says that the transition amplitude $ \langle q_f t_f \vert q_i t_i\rangle $ is $$ ...
5
votes
1answer
137 views

Modern relevance of canonical quantisation [closed]

In some modern field theory texts such as Siegel's Fields it is claimed that canonical quantisation of fields is obsolete as it is not used it modern research papers. Thus, it should be removed from ...
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0answers
46 views

Is Feynmann gauge reduce always physical gauge?

Is Feynmann gauge reduce always physical gauge? I heard in QCD, Feynmann gauge does not always give correct physics. The lecture says, "Fenymann gauge gives physical gauge, if the theory contains ...
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45 views

Doubt in Path integral equation

In Pokorski's "Gauge Field Theories" book, page 108 we find equation (2.87) ...
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0answers
24 views

Green function of squared chiral pseudoscalar in QCD

I need to compute the Green function $$ G(0) \equiv \int d^{4} x\int D[\text{QCD}]\bar{q}\gamma_{5}Mq(x)\bar{q}M\gamma_{5}q(0)e^{iS_{QCD}} \equiv $$ $$ \tag 1 \equiv \int d^{4}x\langle 0|T( ...
4
votes
1answer
67 views

Why use coherent state path integral? What is its motivation or goal?

In almost all textbooks of quantum field theory for high energy, they insert the position and momentum eigenstate to formulate the path integral. While in condensed matter field theory, they insert ...
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0answers
65 views

Theta-parameter vacuum energy

Suppose we have $\theta$-field in QCD (in a special case of constant $\theta$ it reduces to ordinary $\theta$ parameter): $$ \tag 1 Z_{\theta} = \int D[\psi_{QCD}]e^{iS}, $$ where $$ \tag 2 S = \int ...
1
vote
1answer
123 views

Time-ordered product vs path integral

Suppose we have the Green function $$ G(k) \equiv \tag 1\int d^4x e^{ikx}\langle 0| T\left(\partial^{x}_{\mu}A^{\mu}(x)B(0)\right)|0\rangle , $$ which in path integral approach is equal to $$ \tag 2 ...
2
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34 views

Topological susceptibility of electroweak theta-term

Suppose EW theory generating functional: $$ Z[\text{sources}] = \int D(A,\psi,\bar{\psi}, H,H^{\dagger})\text{exp}\bigg[i\int d^{4}x\bigg(-\frac{1}{4g_{EW}^2}F_{EW}^2 + \bar{\psi}(D - m)\psi + ...