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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69 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] ~ \Delta ...
3
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4answers
416 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 ...
6
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1answer
170 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 ...
0
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1answer
63 views

Matsubara Frequencie

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 ...
2
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0answers
48 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}} ...
4
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0answers
60 views

How to calculate gravity path integrals about an AdS background?

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 ...
2
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0answers
50 views

Relationship between the Black-Scholes model and path integrals

This question was inspired by some interesting comments by Rod Vance on this answer: Minkowski spacetime: Is there a signature (+,+,+,+)? Could you (Rod), or someone else, expand on these comments ...
6
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0answers
83 views

Deriving Feynman rules from Renormalized Lagrangian

In the context of Renormalized Pertubation Theory Peskin Schröder says: The Lagrangian $$ \mathcal{L}=\frac{1}{2} (\partial_\mu\phi_r)^2-\frac{1}{2}m^2\phi_r^2-\frac{\lambda}{4!}\phi_r^4 + \frac{1}{2} ...
4
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2answers
115 views

Stationary points of the action functional

In QFT the principle of stationary action states that we choose fields that will make the action stationary but what if the action has many stationary points? What's the significance of these other ...
0
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0answers
42 views

A question about sign in Euclidean path integral

I have a question about the sign in the Euclidean path integral in Polchinski's string theory vol I, p 337. In page 335, Polchinski introduced path integral in Euclidean space $$ \langle q_f, U| ...
2
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1answer
53 views

What is the generating functional for a scalar theory with two different (interacting and real) fields?

My question is specifically about how to use sources? For an interacting theory with one field, one puts a $J(x)\phi(x)$ term in the exponential in the path integral for $W[J]$. I now have two ...
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0answers
57 views

Time-dependent Schrodinger equation from variational principle

In the paper, "Density-functional theory for time-dependent systems" Physical Review Letters 52 (12): 997 the authors mentioned that the action $$ A= \int_{t_0}^{t_1} dt \langle \Phi(t) | i ...
1
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1answer
76 views

Euclidean functional Integrals

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 approximation. To evaluate the ...
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3answers
563 views

The path integral and Feynman diagrams

This question is somewhat of a historical one, but it also contains some physics. I am curious to find how exactly the concept of Feynman diagrams arose (I assume from Feynman's path integral)? The ...
2
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0answers
60 views

Feynman rules of a theory in non-standard form

I am currently studying lecture notes by Akhmedov on interacting scalar field theory in de Sitter space. In these notes, he considers a scalar field theory of the form ...
3
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1answer
107 views

Calculating Tr(log($\Delta_F$))

I am stuck with this problem for quite sometime. I have a propagator in the momentum representation (from this question), which looks like $$ \widetilde\Delta_F(p) = ...
5
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0answers
52 views

What is the probability of a Brownian path?

Suppose I have a Brownian particle with a diffusion constant $D$ starting out from a given position at time $0$ and follow it until time $\tau$. What is the probability (distribution) that it takes ...
5
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0answers
115 views

Casimir Forces and its associated Feynman Propagator

This is a continuation to my previous question, in which I began an attempt solve the Casimir Force problem using path integrals. As one of the answers there suggest I solve the Feynman propagator ...
5
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1answer
133 views

Casimir forces due to scalar field using Path integrals

I have just started learning QFT. I have just completed scalar fields, which I learnt in using Canonical Quantisation and Path integrals. I did calculation of Casimir force between two metal plates ...
6
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1answer
152 views

Does Feynman path integral include discontinuous trajectories?

While reading this derivation of relation of Schrödinger equation to Feynman path integral, I noticed that $q_i$ can differ form $q_{i+1}$ very much, and when the limit of $N\to\infty$ is taken, there ...
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0answers
47 views

path integral quantization of EM field derived from canonical quantization?

In Peskin's QFT book page 294, he formally addressed the quantization of EM field, $$propagotor_{EM}=\frac{-ig_{\mu\nu}}{k^2+i\epsilon}$$ Now that we have the functional integral quantization ...
5
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2answers
210 views

Wick rotation in field theory - rigorous justification?

What is the rigorous justification of Wick rotation in QFT? I'm aware that it is very useful when calculating loop integrals and one can very easily justify it there. However, I haven't seen a ...
2
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1answer
97 views

Functional field integral in condensed matter field theory (Altland)

This is the action for the 1+1 dimensional interacting electron system; $$S_{cl}[\theta , \phi]= \frac{1}{2\pi} \int dxd\tau \left(g^{-1}v(\partial_x \theta)^2 + gv(\partial_x \phi)^2 + ...
4
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1answer
74 views

The correspondence between Grassmann number and 4-spinor

In canonical quantization, we view the Dirac field $\psi$ as a $4\times1$ matrix of complex number. While in path integral quantization, we view the Dirac field $\psi$ as a Grassmann number. For two ...
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0answers
53 views

When can I use semiclassical approximation?

I know that I can use semiclassical approximation for path integral approach (in quantum mechanics) $\int d[q]e^{iA}$ when action $A >>1 $. But how shall I use such condition? For example, ...
10
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1answer
213 views

Can nowadays spin be described using path integrals?

In Feynmans book, "Quantum mechanics and Path Integrals" he writes in the conclusions (chapter 12-10) With regards to quantum mechanics, path integrals suffer most grievously from a serious ...
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100 views

Functional integral aproach for Feynman rules

I am familiar with the basic ideas of quantum field theory but I feel uncomfortable when I have to derive Feynman rules by myself for a given action (for example in non-linear sigma models or ...
3
votes
2answers
179 views

Connection between QFT and statistical physics of phase transitions

I have heard that there is a deep connection between QFT (emphasized by its path-integral formulation) and statistical physics of critical systems and phase transitions. I have only a basic course in ...
3
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1answer
165 views

Paths in the path integral

In the path integral approach one defines in some heuristic way the functional path integral \begin{equation} Z=\int{\cal{D}}\phi e^{iS(\phi)} \end{equation} and the one claims that one must ...
4
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1answer
191 views

From Minkowski to Euclidean Time in Path Integrals

I'm trying to prove the following equality: $$ <x_{f},\, it_{f}|x_{i},\, it_{i}>=\mathcal{N}\int_{\left\{ x\in\mathbb{R}^{\mathbb{R}}:\, x\left(t_{f}\right)=x_{f}\wedge ...
3
votes
1answer
145 views

Free particle propagator - Evaluating Integral [closed]

In path integral formalism, when evaluating the free particle propagator, we obtain the functional integral of the form, $$ K_0 = \lim_{n\rightarrow\infty} \bigg( \frac{m}{2\pi ...
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0answers
82 views

Good introduction to many-body Green's function via path integral formulation?

Can anyone kindly provide any information on valuable references or books on this topic? It appears to be prevalent in 90s papers on High-Tc superconductivity or quantum Hall effect, especially in a ...
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0answers
77 views

How simplify functional derivatives (in path integrals) with mathematica?

Are there any packages that can simplify functional derivatives in path integrals? For instance the expression (integrate over, $x,y,z,u,v,r,s$): ...
0
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1answer
166 views

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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0answers
32 views

Path Integral back in time

For the non relativistic path integral we have to consider all contributions of all paths that connect two space-time coordinates, form $(\mathbf{x}_0,t_0)$ to $(\mathbf{x}_1,t_1)$. Are there also the ...
3
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1answer
158 views

Path integral as a functional determinant

In Peskin and Schroeder on pg. 304, the authors call the fermionic path integral: \begin{equation} \int {\cal D} \bar{\psi} {\cal D} \psi \exp \left[ i \int \,d^4x \bar{\psi} ( i \gamma_\mu D^\mu - m ...
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134 views

Divergent path integral

What does it mean to have a divergent path integral in a QFT? More specifically, if $$\int e^{i S[\phi]/\hbar} D\phi (t)=\infty $$ What does this mean for the QFT of the field $\phi $? The field ...
2
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1answer
99 views

Adding stuff to the path integral (Faddeev-Popov method)

I'm wondering about the Faddeev-Popov method described in Peskin Schroeder and also on page 7 in this link. What gives them the right to simply add the Gaussian $\omega$ and thus introduce the $\xi$ ...
3
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1answer
93 views

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. ...
8
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1answer
211 views

Sign in the photon propagator

The Klein Gordon propagator is given (I use Peskin and Schroeder's conventions, if it matters...), \begin{equation} \frac{ i }{ p ^2 - m ^2 + i \epsilon } \end{equation} The photon propagator ...
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0answers
54 views

Global anomaly for discrete groups

We know that: a global anomaly is a type of anomaly: in this particular case, it is a quantum effect that invalidates a large gauge transformations that would otherwise be preserved in the ...
2
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1answer
101 views

Quick-and-dirty way to integrate out heavy fields

I understand the roughly understand the process of integrating out heavy degrees of freedom of a Lagrangian, namely, taking the action and performing the path integral over the high momentum modes. ...
8
votes
1answer
364 views

Green's function in path integral approach (QFT)

After having studied canonical quantization and feeling (relatively) comfortable with it, I have now been studying the path integral approach. But I don't feel entirely comfortable with. I have the ...
2
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0answers
236 views

Looking for solutions to problems in Feynman and Hibbs path integral and QM text [closed]

I've just started reading Feynman and Hibbs path integrals and Quantum mechanics after a decade hiatus from my undergraduate math degree (including a few semesters of physics for engineers). It would ...
3
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0answers
71 views

What is the point of path integral for boson and fermion?

I am a beginner to study QFT and confused about path integral for boson or fermion. I have read about the path integral for single particle, and finished some problems. But I cannot understand the ...
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0answers
67 views

Quantum mechanics formulations [closed]

There are about 9 different formulations of quantum mechanics. What are the merits and setbacks of each formulation? In the path integral formulation, is the sum over all possible paths idea purely ...
2
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1answer
118 views

Ghost fields in particle physics

In my particle physics lecture, ghost fields were briefly mentioned. As far as I understand, these come up when computing cross sections by the path integral method, to compensate for equivalent ...
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2answers
154 views

Can path integral paths go backwards in time?

The paths can cross any coordinate at any time in the whole space (e.g. Universe space). Integration goes over all could-you-imagine paths. But time goes strictly forward. Can time variable resemble ...
6
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2answers
234 views

Interpretation: probability form probability amplitude (free particle)

If you compute the probability amplitude of a free 1D non-relativistic particle with mass $m$, located at position $x_0$ at time $t_0$, for beeing detected at some other point $x_N$ at time $t_N$ you ...
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4answers
942 views

How exact is the analogy between statistical mechanics and quantum field theory?

Famously, the path integral of quantum field theory is related to the partition function of statistical mechanics via a Wick rotation and there is therefore a formal analogy between the two. I have a ...