Linked Questions
21 questions linked to/from Wick rotation in field theory - rigorous justification?
3
votes
0
answers
73
views
Can the QFT path integral be re-expressed using a real, positive-definite function of the action? [duplicate]
This question is based on my rather shaky grasp of QFT, so if I'm missing a key concept then just let me know!
If you're deriving the Schrodinger equation from the path integral as Feynman did, then ...
- 2,587
1
vote
0
answers
47
views
Physics in Euclidean spacetime [duplicate]
I just have a very small and naive Question.
In my PhD I work on different Toy models which are implemented on the lattice.
In order to do so one performs a Wick rotation from minkowski to euclidean ...
- 11
128
votes
4
answers
15k
views
The Role of Rigor [closed]
The purpose of this question is to ask about the role of mathematical rigor in physics. In order to formulate a question that can be answered, and not just discussed, I divided this large issue into ...
- 2,113
65
votes
7
answers
17k
views
Rigor in quantum field theory
Quantum field theory is a broad subject and has the reputation of using methods which are mathematically desiring. For example working with and subtracting infinities or the use of path integrals, ...
- 3,855
29
votes
2
answers
14k
views
Gaussian integral with imaginary coefficients and Wick rotation
Although this question is going to seem completely trivial to anyone with any exposure to path integrals, I'm looking to answer this precisely and haven't been able to find any materials after looking ...
- 1,774
22
votes
3
answers
5k
views
Problems while Wick rotating the path integral
I am trying to begin from the path integral of QM and write the Euclidean version of it performing the Wick rotation but it seems that I am missing a few things.
For simplicity I work on 1 dimension ...
- 6,137
12
votes
2
answers
1k
views
Why isn't Quantum Yang-Mills Rigorous?
Obviously one of the major components of the Yang-Mills existence and mass gap problem of the Clay institute is the proof that 3+1d quantum yang-mills theory has rigorous foundations. This (I believe) ...
- 301
28
votes
2
answers
3k
views
Wick rotation and spinors
I am quite familiar with use of Wick rotations in QFT, but one thing annoys me: let's say we perform it for treating more conveniently (ie. making converge) a functional integral containing spinors; ...
- 2,926
6
votes
1
answer
667
views
Proving that a Wick rotation is valid for a quantum field theory
While trying to find out if there is a rigorous justification for Wick rotating a QFT, I came across this other question (link below [1]) that mentions the Osterwalder-Schrader Theorem that gives a ...
- 733
3
votes
2
answers
808
views
Invariance in Euclidean and Minkowski spaces
Consider Wick's rotation from Minkowski to Euclidean space in QFT. What is the connection between $O(4)$-invariance in Euclidean space and Lorentz invariance in Minkowski space? If we define a ...
- 41
4
votes
1
answer
466
views
In QFT, why are the vacuum partition function and the zero-temperature imaginary-time partition function the same?
When doing thermal field theory, one can start with the definition of the (thermal) partition function $Z = Tr[e^{-\beta H}]$, and inserting a number of completness-relations, we can arrive at (I am ...
- 577
2
votes
0
answers
856
views
Euclidean QFT definition
I have a question on Euclidean field theories and their relationship with QFT defined on a Minkowski spacetime.
In order to compute the generating function $Z$, one has to compute the integral
$$Z = ...
- 349
4
votes
0
answers
503
views
Is Wick rotation of loop integrals legitimate?
In Feynman diagram calculations, we seem to invariably Euclideanise loop integrals in order to exploit the resulting spherical symmetry. This Wick rotation is simply a deformation of the contour; ...
- 6,515
2
votes
1
answer
354
views
Why do we Wick rotate before regularizing Feynman diagrams?
In Folland's Quantum Field Theory he mentions that we can apply Feynman's formula (Feynman parameterization) to either the Wick rotated integrals or the non-Wick rotated integrals corresponding to ...
- 3,992
2
votes
1
answer
216
views
Examples of Path integral $\neq$ Partition function?
Are there any systems we know of whose partition function is not simply Wick rotation of the path integral? Does anyone know of any examples?
- 1,415