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Results tagged with mp.mathematical-physics
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user 7410
Mathematical methods in classical mechanics, classical and quantum field theory, quantum mechanics, statistical mechanics, condensed matter, nuclear and atomic physics.
31
votes
Why is Quantum Field Theory so topological?
The framing of your question is a bit ambiguous and perhaps there are two different questions
here depending on the context and interpretation. One could approach your question from the point of view …
30
votes
What mathematical treatment is there on the renormalization group flow in a space of Lagrang...
Dec 2017 edit: I just put a hopefully useful detailed complement to this post on https://physics.stackexchange.com/questions/372306/wilsonian-definition-of-renormalizability
The answer to your ques …
30
votes
A roadmap to Hairer's theory for taming infinities
Let me comment on points 4) and 5). The problem with infinities in QFT or traditional equilibrium statistical field theory
is related to the one addressed by Martin's theory but there are some differe …
25
votes
Mathematical applications of quantum field theory
@Sarah:
I have some reservations about how the question is framed since it already answers itself and makes QFT seems like a subject which is completely separate from mathematics with occasional and a …
25
votes
$p$-adic numbers in physics
Since the question on physics.stackexchange that was referred to in the comments above has been closed, let me essentially repeat my answer here together with some updates.
I think there are mainly …
20
votes
Accepted
Formal mathematical definition of renormalization group flow
The renormalization group (RG) as a geometric flow (like the Ricci flow) is a very
special case of the RG, namely, the one corresponding to the nonlinear sigma-model (NLSM) in two dimensions with valu …
18
votes
Why is conformal invariance only possible for massless theories?
It's not clear from the post if you are talking about classical or quantum field theories. In QFT, conformal invariance implies scale invariance. If the theory has a mass $m$ then, as John explained, …
15
votes
Standard model of particle physics for mathematicians
An excellent introduction for a mathematician without previous exposure to quantum field theory is the book by Gerald Folland:
"Quantum field theory, a tourist guide for mathematicians", ISBN: 978-0-8 …
15
votes
Accepted
Mathematical predictions of AdS/CFT
Although it might seem futile, given how far most of the activity on AdS/CFT is from rigorous mathematics, I think this a good question, provided one is happy, for now, with (very) baby versions of th …
15
votes
The Unreasonable Effectiveness of Physics in Mathematics. Why ? What/how to catch?
It seems to me the answer to:
"Do physicists have some tools/ideas/techniques which allow them to make insights, which are not seen for mathematicians?" is indeed yes. Not only such a tool exists but, …
13
votes
4d Constructive Quantum Field Theory
Modern constructive field theory is based on rigorous implementations of the renormalization group (RG) approach. To get an idea of what this is about see
this short introductory paper.
The RG is an i …
12
votes
Accepted
What is the role of topology on infinite dimensional exterior algebras?
Focusing on exterior powers here is a distraction. The main problem already appears when considering the tensor algebra $T(E)=\oplus_{n\ge 0}E^{\otimes n}$. Once the issue is understood for the tensor …
12
votes
Is there a program to solve The Yang–Mills Existence and Mass Gap problem similar to the Ham...
Coming a bit late to the party, but since there is no answer, let me offer one.
Yes there is a program to make progress towards the YM problem, although with no guarantee of success in the end. The me …
10
votes
Free Boson Correlator $ \langle X(z)X(w) \rangle =- \ln |z - w| $
My answer Wiener measure and Bochner Minlos can help defining a free massless real scalar field as a random element of $S_0'(\mathbb{R}^2)$. Namely, take the Schwartz space of rapidly decaying test fu …
10
votes
Simple example of renormalization
The simplest and earliest example I know regarding the
renormalization group idea is the following.
Suppose we
want to study some feature $\mathcal{Z}(\vec{V})$ of some object $\vec{V}$
which is in a …