DO NOT USE THIS TAG just because your question involves math! If your question is on simplification of a mathematical expression, please ask it at math.stackexchange.com Mathematical physics is the mathematically rigorous study of the foundations of physics, and the application of advanced ...
3
votes
0answers
51 views
Reference Request: Classical Mechanics with Symplectic Reduction [closed]
I am trying to find a supplement to appendix of Cushman & Bates' book on Global aspects of Classical Integrable Systems, that is less terse and explains mechanics with Lie groups (with dual of Lie ...
5
votes
3answers
197 views
Why is this identity an if, rather than if and only if?
A recent question (Product of exponential of operators) asked who to proved that the exponentials of operators multiply in same manner as those of scalars if and only if the commutator of the ...
5
votes
3answers
215 views
What is a dual / cotangent space?
Dual spaces are home to bras in quantum mechanics; cotangent spaces are home to linear maps in the tensor formalism of general relativity. After taking courses in these two subjects, I've still never ...
2
votes
3answers
271 views
Results of Statistical Mechanics first obtained by formal mathematical methods
I have a question that seems natural in Physics and Mathematics mainly in Statistical Mechanics of Equilibrium.
Results that are proven by formal mathematical methods that were already seem intuitive ...
4
votes
0answers
67 views
Electric potential of a spheroidal gaussian
I'm looking for results that compute the electrostatic potential due to a spheroidal gaussian distribution. Specifically, I'm looking for solutions of equations of the form
$$
...
2
votes
2answers
145 views
Infinitely many planets on a line, with Newtonian gravity
(I apologize if this question is too theoretical for this site.)
This is related to the answer here, although I came up with it independently of that. $\:$ Suppose we
have a unit mass planet at each ...
1
vote
3answers
171 views
Is a quantum system mandatory for generating true random sequence?
Is a quantum system necessary if we want to generate true random sequence? The mathematical framework used for classical mechanics doesn't involve any random value. But the mathematical framework of ...
4
votes
1answer
137 views
The use of Hall algebras in physics
I asked the same question in mo. I think maybe here there are more physics guys to help me.
I once read a statement (not memorized precisely) that a certain physics quantity between two states of ...
2
votes
1answer
93 views
Does a constant of motion always imply a Hamiltonian formulation?
If a continuous dynamical system has a constant of motion that is a function of all its variables, and is not already evidently Hamiltonian, is it always possible to use a change of variables and ...
1
vote
1answer
54 views
Can I prove boundedness of an operator without checking it for its whole domain?
(I don't have a direct reference so this is a little fishy and I'll delete it if nobody recognises what I'm talking about, but I though for starters I'll ask anyway)
I've heard at university that if ...
2
votes
2answers
276 views
Greens function in EM with boundary conditions confusion
So I thought I was understanding Green's functions, but now I am unsure. I'll start by explaining (briefly) what I think I know then ask the question.
Background
Greens are a way of solving ...
5
votes
3answers
1k views
Can Laplace's equation be solved using Fourier transform instead of Fourier series?
Sorry for the long text, but I am unable to make my question more compact.
Any periodic function can be Fourier expanded. Usually, they say in mathematical physics books, if the function is not ...
3
votes
0answers
206 views
Mathematics and Physics prerequisites for mirror symmetry [closed]
I am a physics undergrad interested in Mathematical Physics. I am more interested in the mathematical side of things, and interested to solve problems in mathematics using Physics. My current ...
10
votes
3answers
322 views
Representing forces as one-forms
First of all, sorry if any of those things are silly or nonsense, I'm just trying to understand better how the concepts of forms, exterior derivative and so on can be used in physics.
This question ...
2
votes
1answer
69 views
Electric force on spherical surface
I have a doubt about electrical forces on surfaces, for instance, on the surface of a sphere. I'll explain my point: let's say we have some spherical surface of unit radius and there's one point ...
1
vote
2answers
406 views
Geodesics and trajectories
I'm a mathematician studying Arnold's Mathematical Methods of Classical Mechanics.
On p. 83 the following definition is given.
Let $M$ be a differentiable manifold, $TM$ its tangent bundle, and ...
5
votes
3answers
407 views
What is the relation between (physicists) functional derivatives and Fréchet derivatives
I´m wondering how can one get to the definition of Functional Derivative found on most Quantum Field Theory books:
$$\frac{\delta F[f(x)]}{\delta f(y) } = \lim_{\epsilon \rightarrow 0} ...
5
votes
6answers
758 views
Laplacian of $1/r^2$ (context: electromagnetism and poisson equation)
We know that a point charge $q$ located at the origin $r=0$ produces a potential $\sim \frac{q}{r}$, and this is consistent with the fact that the Laplacian of $\frac{q}{r}$ is
...
10
votes
1answer
225 views
Witten's constrained S-matrix and Coleman-Mandula Theorem
I remember reading somewhere that Witten argued that if the Poincaré symmetry of spacetime were nontrivially combined with internal symmetries, then the S-matrix would be so constrained that the ...
8
votes
2answers
489 views
Introductory texts for functionals and calculus of variation
I am going to learn some math about functionALs (like functional derivative, functional integration, functional Fourier transform) and calculus of variation. Just looking forward to any good ...
2
votes
1answer
110 views
Physical Significance of Operator Norm/Spectral Norm of a Quantum Operator
Is there any physical significance of operator norm/spectral norm of a hermitian operator?
4
votes
1answer
230 views
First Chern number, monoples and quantum Hall states
The first Chern number $\cal C$ is known to be related to various physical objects.
Gauge fields are known as connections of some principle bundles. In particular, principle $U(1)$ bundle is said to ...
6
votes
1answer
167 views
“An operator is hermitian”. Implications?
Alastair Rae states that there are 4 postulates of Quantum Mechanics in his text on the subject matter. The first part of his second postulate can be stated as:
Every dynamical variable may be ...
4
votes
1answer
146 views
How do we make symmetry assumptions rigorous?
I have, for instance, a problem with a spherically symmetric charge distribution. I deduce here, in order to solve the problem easily, that the corresponding electric field must be symmetric. How is ...
4
votes
2answers
343 views
Book covering Topology required for physics and applications
I am a physics undergrad, and interested to learn Topology so far as it has use in Physics. Currently I am trying to study Topological solitons but bogged down by some topological concepts. I am not ...
3
votes
4answers
477 views
Topology needed for Differential Geometry [duplicate]
I am a physics undergrad, and need to study differential geometry ASAP to supplement my studies on solitons and instantons. How much topology do I need to know. I know some basic concepts reading from ...
25
votes
10answers
4k views
Best books for mathematical background?
What are the best textbooks to read for the mathematical background you need for modern physics, such as, string theory?
Some subjects off the top of my head that probably need covering:
...
1
vote
1answer
104 views
Topology for physicists [duplicate]
Which are the best introductory books for topology, algebraic geometry, manifolds etc, needed for string theory?
7
votes
8answers
586 views
Mathematical Universe Hypothesis
What is the current "consensus" on Max Tegmark's Mathematical Universe Hypothesis (MUH) which claims every concievable mathematical structure exists, including infinite different Universes etc.
I ...
0
votes
0answers
58 views
Is there a book that discusses General Relativity in terms of Modern Differential Geometry? [duplicate]
All of the physics books that I've seen which discuss General Relativity do so in terms of coordinates - the tensor calculus - even though the naturally relevant entities are invariant under general ...
51
votes
6answers
844 views
What are the justifying foundations of statistical mechanics without appealing to the ergodic hypothesis?
This question was listed as one of the questions in the proposal (see here), and I didn't know the answer. I don't know the ethics on blatantly stealing such a question, so if it should be deleted or ...
6
votes
1answer
128 views
Are group representations possible when the solution space is not a vector space?
As far as I understand, the motivation for using representation theory in high energy physics is as follows. Assume that a theory has some (internal or external) symmetry group which acts on a vector ...
10
votes
2answers
886 views
Applications of the Spectral Theorem to Quantum Mechanics
I'm currently learning some basic functional analysis. Yesterday I arrived at the spectral theorem of self-adjoint operators. I've heard that this theorem has lots of applications in Quantum ...
6
votes
2answers
536 views
Sources to learn about Greens functions
For a physics major, what are the best books/references on Greens functions for self-studying?
My mathematical background is on the level of Mathematical Methods in the physical sciences by Mary ...
2
votes
0answers
73 views
Physics textbook for mathematicians [duplicate]
Before this post gets marked as duplicate, I've checked book book recommendations among other posts but I don't think they really answer this fairly niche question.
I am looking to compile a list of ...
6
votes
1answer
110 views
precise definition of “moduli space”
I'm curious what the precise definition of the moduli space of a QFT is. One often talks about the classical moduli space, which then can get quantum corrections. Does this mean the quantum moduli ...
6
votes
2answers
91 views
fitting free QFTs into the Haag-Kastler algebraic formulation
Has the free Klein-Gordon quantum field theory been fitted into the
Haag-Kastler algebraic framework? (Actually, John Baez told me "yes", and he should know.) If so, can you describe the basic
...
1
vote
1answer
151 views
What is the mathematical background needed for quantum physics? [duplicate]
I'm a computer scientist with a huge interest in mathematics. I have also recently started to develop some interest about quantum mechanics and quantum field theory. Assuming some knowledge in the ...
2
votes
5answers
3k views
Mathematical background for Quantum Mechanics
What are some good sources to learn the mathematical background of Quantum Mechanics?
I am talking functional analysis, operator theory etc etc...
4
votes
1answer
308 views
A confusion from Weinberg's QFT text (a vanishing term in Lippmann-Schwinger equation)
I was reviewing the first few chapters of Weinberg Vol I and found a hole in my understanding in page 112, where he tried to show in the asymptotic past $t=−∞$, the in states coincide with a free ...
7
votes
2answers
201 views
Advice on doing physics under the umbrella of mathematics and the converse
In the current scenario of research in QFT and string theory (and related mathematical topics), which of the following would an undergraduate student, like me, be advised to do and why if s/he is ...
18
votes
1answer
286 views
Geometric picture behind quantum expanders
A $(d,\lambda)$-quantum expander is a distribution $\nu$ over the unitary group $\mathcal{U}(d)$ with the property that: a) $|\mathrm{supp} \ \nu| =d$, b) $\Vert \mathbb{E}_{U \sim \nu} U \otimes ...
3
votes
3answers
182 views
Is there a mathematical relationship here or am I looking for relations when there are none?
When I was taking classical mechanics, we dealt a lot with pendulums, and orbiting bodies problems. This lead me to think about the two situations depicted above. Left: Shows two balls of equal mass ...
9
votes
2answers
570 views
Are there books on Regularization and Renormalization in QFT at an Introductory level?
Are there books on Regularization and Renormalization, in the context of quantum field theory at an Introductory level? Could you suggest one?
Added: I posted at math.SE the question Reference ...
2
votes
2answers
221 views
Differentiation and delta function
Need help doing this simple differentiation.
Consider 4 d Euclidean(or Minkowskian) spacetime.
\begin{equation}
\partial_{\mu}\frac{(a-x)_\mu}{(a-x)^4}= ?
\end{equation}
where $a_\mu$ is a constant ...
5
votes
2answers
1k views
Limit of Lorentzian is Dirac Delta
I have a quick question that just came up in my research and I could not find an answer anywhere so I thought I'd try here.
So one of the definitions of the Dirac Delta is the limit of the Lorentzian ...
0
votes
2answers
105 views
From differentials to differential equations
Suppose I have a function of time $t$ and position $(x,y)$ such that
\begin{equation} p_t \,dt = p \,dy - p_x (1-x) \,dx + p_y \,dy\end{equation}
where the subscript denotes a differentiation. In this ...
1
vote
0answers
188 views
Apostol or Spivak for mathematical physics? [closed]
I came across many recommendations for both of these books, but I'm not sure which one should I use to study calculus...
I know most of the methods used in calculus and I use them frequently, but I'm ...
4
votes
1answer
34 views
Tip of a spreading wave-packet: asymptotics beyond all orders of a saddle point expansion
This is a technical question coming from mapping of an unrelated problem onto dynamics of a non-relativistic massive particle in 1+1 dimensions. This issue is with asymptotics dominated by a term ...
2
votes
1answer
114 views
electrostatic potential, analytic properties
An electrostatic potential associated with some delocalized charge $\int \rho(\mathbf{r}) d{\mathbf{r}}$ is given by:
$$v_H(\mathbf{r}) = \int ...
