# Questions tagged [mathematics]

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 The mathematics tag covers non-applied pure mathematical disciplines that are traditionally not part of the mathematical physics curriculum, such as, e.g., number theory, category theory, algebraic geometry, general topology, algebraic topology, etc.

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1answer
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### Exponent of tensor product of operators (context: weak measurement)

I'm stuck on some identity for an exponentiated tensor product of operators, $e^{\hat A\otimes\hat B}$. I'm learning weak measurement, reading the review by Kofman et al (2012, DOI: 10.1016/j.physrep....
2answers
37 views

### How to fit the data for the asymptotic limit?

Suppose we have a pretty good experiment data with very small random error. But our theory is limited, which makes the systematic error significant. Sometimes we do have a nice theory for the weak ...
0answers
41 views

### infinitesimal areas and large areas scalar or vector quantities? [duplicate]

Is it true that an infinitesimal area is a vector quantity and large area is a scalar quantity ?
0answers
22 views

### Measure theory and fractal measure

I want to study multifractal for turbulent but I need to learn measure theory for this. so I wanna introduce me some book for both?
3answers
300 views

### How to write down various metrics without coordinates?

For example Schwarzschild metric, or Alcubierre metric, but using only intrinsic (natural, canonical, etc.) physical objects (like length, angles, etc.) for relations between natural objects on ...
1answer
21 views

### A question on the transition matrix. (algebraic derivation)

I am trying to follow the derivation of the following identity: $$[\epsilon -H_0+i\eta]^{-1}T = [\epsilon - H +i\eta]^{-1}U$$ where $T$ is the transition matrix and $U$ is the potential caused by ...
1answer
126 views

### Is there an explanation for this unexpected similarity between binomial coefficients and waves?

Background Binomial coefficients appeal mostly in probability, combinatorics number theory etc so were were surprised when we observed something that appeared to belong more to physics than pure ...
1answer
94 views

### Could a reformulation of GR and QFT in terms of nonstandard analysis be useful?

Are there any serious reformulations of a quantum field theory of general relativity within a nonstandard analysis framework?  Is it possible that such reformulations (which are possible,  in ...
3answers
87 views

### Trouble with Math in Physics [duplicate]

I am a current high school student and I am very interested in physics, especially particle physics (that stuff is super cool!). Unfortunately, my school only teaches classical physics, so I have to ...
2answers
46 views

### How many linear combinations of harmonics or normal modes can describe the same periodic function as a Fourier series?

Please note that I am not asking how many terms in a linear combination can describe a specific periodic function but if given that there exist a set or linear combination of normal modes that ...
2answers
125 views

### Is $[A,\exp{B}]=0 \Rightarrow [A,B]=0$ true?

The backward direction is trivial and this one probably too, but I just can't find a convincing argument. $A$, $B$ are Operators on a Hilbert Space (Ket Space).
1answer
46 views

1answer
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### Derivative of tensor product of quantum states

Recently I asked a question over at the math stack exchange: https://math.stackexchange.com/q/3210375/. However I figured I'd ask here too, seeing as the question originated in a physics course I'm ...
2answers
93 views

### Infinite sum: Renormalisation

Trying to do the calculation made in a physics article Real-time Feynman path integral with Picard--Lefschetz theory and its applications to quantum tunneling (page 10 to go from equation 56 to 57), I ...
0answers
79 views

### Characteristics of the Navier-Stokes equations as a set of PDE's

I am not entirely sure if I should ask this question here or not, but here goes: can anyone suggest any reference (book, article, etc.) about the Navier-Stokes equations from a mathematical point view?...
0answers
20 views

### Which books or content should I prefer to understand particle physics operator and representations [duplicate]

I am just a intermediate passout and I want to know which books should I prefer for learning the mathematics of particle physics level like the different representation, operation like Hamiltonian, ...
1answer
50 views

### Is curvature the exterior covariant derivative of the connection?

Let $P\to M$ be a $G$-principal bundle, $G$ a topological group, $\omega$ the connection and $V$ a vector space. We define $d_\omega: \Omega^k_G(P, V)\to\Omega^{k+1}_G(P, V)$ the exterior covariant ...
2answers
117 views

### Precise definition of the Hilbert space in QM?

In QM books (at least those I have read) the definition of the Hilbert space used is somewhat blurred (the "space of square integrable functions" is not enough to define it precisely : which kind of ...
2answers
307 views

### Does it make sense to speak in a total derivative of a functional? Part I

I would like to consider the problem of the total derivative of a given functional \begin{equation} \mathcal{L}\bigg[\phi\big(x,y,z,t\big),\frac{\partial{\phi}}{\partial{x}}\big(x,y,z,t\big),\frac{\...
1answer
81 views

### Dirac delta function mathematical expression proof

In a discussion of the second order transitions in graphene this mathematical expression is used. $$\left|\frac{1}{\varepsilon + i \Gamma/2}\right|^2 = \frac{2\pi}{\Gamma}\delta(\epsilon)$$ And I'm ...
1answer
107 views

### Is math truly infinite or is it just theory? [closed]

I imagine you can theoretically add +1 to any number But untill it happens it isnt so. That + no free will = math is limited and has a definite value. I imagine its tied in with conservation laws... ...
0answers
41 views

### How to prove that the limit of surface integral exists?

My book "Electromagnetic Fields" says in $\text{Section}\ 3.4$: Question Why does the limit in equation $(3.42)$ exist (convergent)? Why is the contribution from $(S-S_{\delta})$ remains ...
0answers
44 views

### A. Zee Contour Integral

In A.Zee's book I have come a cross an integral which I found difficult to solve.
2answers
86 views

### What are the theorems that constitute the Maxwell's equation? [closed]

Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. ...
2answers
120 views

### Non-rigorous math books [duplicate]

I’m self-studying physics and mathematics out of interest and I am looking for some non-rigorous (text)books on mathematics. Perhaps one book covering all areas relevant to physics or separate books ...
1answer
81 views

### Diffusion equation with time-dependent boundary condition

I was trying to solve this 1D diffusion problem \begin{equation} \dfrac{\partial^2 T}{\partial \xi^2} = \dfrac{1}{\kappa_S}\dfrac{\partial T}{\partial t}\, , \label{eq_diff_xi} \end{equation} with ...
1answer
75 views

### Do non-abelian group mathematics have any use in the real world math? [closed]

I know physics uses a lot of non-abelian mathematics (though I cannot wrap my head around ab does not equal ba).. Is there any real world (macro world we live in) uses for non-abelian mathematics? ...
0answers
35 views

### Is there an easier guide or something to George Arfken's mathematical methods for physicists? [duplicate]

I'm doing bachelor's in Physics and in 3rd semester the professor introduced Mathematical methods with us, which seemed like a great book at first but by the time we started a chapter on Tensor ...
2answers
151 views

### Complex conjugated representation and its Young tableaux

This post is an exact copy of one that I posted in Math's site. I do this copy because people there suggested me to do it since, apparentely, in Mathematics and Physics we use different conventions ...
0answers
99 views

### Euler-Maclaurin formula for path integral

Is there a corresponding Euler-Maclaurin formula for path integral when we divide the path integral into discrete lattice? What is the error correction when we divide the space into lattice of length ...