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 ...

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2answers
23 views

Counting classical microstates

In my notes it states that the convention for summing over the classical states is $$\sum_{\Gamma} \longrightarrow \frac{1}{N!}\int \prod_{i=1}^N \frac{d^3q_id^3p_i}{h_0^3} \tag1$$ Now I know that ...
1
vote
2answers
163 views

Number of microstates compatible with two boxes

From my notes I have: From one point of view there are many more microstates compatible with the LHS than the RHS, in fact the relation between the number of microstates is ...
0
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0answers
47 views

how to define infinite/finite systems in nature? [on hold]

Infinity may be fixed and limited in a set, sequence, or series to repeat the same things infinitely and the finite is not fixed/unlimited to repeat different things finitely. Both can be described by ...
2
votes
2answers
46 views

Can I take the partial derivative of the Lagrangian with respect to a constant?

I've got a system where I know that the derivative of one of the generalized coordinates is constant. So to find the Hamiltonian of the system I need to take the partial derivative with respect to ...
0
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0answers
22 views

How to convert $V \otimes W^*$ to a matrix space? [migrated]

Namely let's say we have chosen basises $e_1, e_2, ... e_k$ for $V$ and $j_1, j_2, ... j_n$ for $W$. Now, since we can always just convert them separately, and then add the matrixes, how we represent ...
3
votes
1answer
263 views

Why are three parameters required to express rotation in 3 dimension?

We know that in spherical coordinates angle $\theta$ and $\phi$ (two angles)are enough to express three dimensional rotation of matrix. But to express rotation mathematically as a transformation ...
1
vote
1answer
39 views

Every Galilean transformation can be written as the composition of rotation, translation, and uniform motion

Having heard many good things about Arnold's Mathematical Methods of Classical Mechanics, I picked it up and started going through it. While I think I understand all of the definitions he makes, the ...
1
vote
1answer
36 views

Description of charged sphere with Heaviside function in cylindrical coordinates

I need to describe density of charge of uniformly charged sphere (radius R, total charge Q, position of centre (0,0,0)) with Dirac delta function and Heaviside step function. The hard part is to ...
0
votes
1answer
51 views

Requirements prior to Quantum Mechanics [duplicate]

What are the requirements in physics and mathematics that somebody must have in order to start learning Quantum Mechanics by himself?
2
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4answers
71 views

Dual of the TDSE

Quite a quick and hopefully simple question. The TDSE takes the form $$i\hbar\frac{\partial\lvert\psi\rangle}{\partial t}=H\lvert\psi\rangle$$ and so if we take the dual of this to find the time ...
14
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2answers
1k views

Can quaternion math be used to model spacetime?

Quaternions are commonly used to model 4 dimensional systems where the quaternion consists of a real 3 dimensional vector and an imaginary scalar. So on the surface Quaternions seem well suited to ...
1
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0answers
49 views

Justifying the use of real numbers for measuring length

I am not sure if this is the most appropriate place to post this but here goes nothing: Assume we were trying to come up with system of numbers $S$ to model our intuition of length. We want $S$ to ...
4
votes
1answer
99 views

Which cardinality of infinities are subtracted in the renormalisation of quantum field theory?

In quantum field theory, e.g. in quantum electrodynamics, renormalisation is used to make sense of an infinite number of virtual particles. This, crudely, involves the subtraction of infinities. But ...
0
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0answers
31 views

Gauge invariance and non-commuting second derivatives

I'm currently doing a homework assignment in relativistic quantum mechanics, and one of the problems involves proving the gauge invariance of a particular lagrangian. The problem is really quite ...
0
votes
2answers
53 views

Calculating the electric field of an infinite flat 2D sheet of charge

I was trying to calculate the electric field of an infinite flat sheet of charge. I considered the sheet to be the plane $z=0$ and the position where the electric field is calculated to be ...
0
votes
1answer
53 views

What is the relationship between completeness of wave functions and completeness of Hilbert space?

In the lecture, my prof said that completeness means that any wave function can be constructed using an infinite number of "other" basis wave functions. This is very intuitive since this is nothing ...
1
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0answers
33 views

Solving inhomogeneous Stokes equation

I want to solve the Stokes inhomogeneous equation, i.e. $$\nabla^2 \vec v -\nabla P = \vec f(r,\theta)$$ $$\nabla\cdot\vec v=0$$ where $\vec f$ is irrotational, i.e. $\partial_y f_x - \partial_x ...
0
votes
1answer
41 views

Role of math in science [closed]

Is it important for a physicist to be good at math? Should he be on par with a mathematician? According to me physics and math are like English and biology we study them in the same language but they ...
0
votes
0answers
40 views

Algebraic number theory and physics [duplicate]

I would like to ask if there are any aspects of algebraic number theory related to physics (for example in string theory or Moonshine etc). I am thinking of attending a course on algebraic number ...
3
votes
2answers
435 views

Hilbert's sixth problem (current answers neglect the fact that $C_{U} \subseteq U $ ) [duplicate]

(current answers neglect the fact that the set of all concepts( $C_{U}$) is a subset of U as all of them are physically encoded( symbolically represented by the physical events themselves(brains, ...
0
votes
2answers
116 views

Significance of $\pi$ in physics

We all know this magical mathematical constant. My question being , how and why pi just shows up in every other physics derivation or formula or even statistics for that matter . ...
0
votes
2answers
103 views

Study material for quantum mechanics [duplicate]

I want to study quantum mechanics. But I don't know what and which topics of mathematics are required. I know a bit of differential calculus. But what else is needed to study a bit advanced quantum ...
0
votes
0answers
54 views

Good book for learning about mathematical foundation of quantum physics [duplicate]

I've been trying to slog through Quantum Physics for Dummies, but can't even get past the first chapter. There's a lot of talk of Bras, Kets, and Hilbert spaces, but I feel I'm missing the ...
0
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0answers
41 views

Simple math used for physics

I read the book "Analysis 1" by Harro Heuser about calculus and it several interesting chapters about applications of mathematics for physics. For example there was one part of the chapter, which ...
2
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0answers
93 views

The implications of Gödel's Second Incompleteness Theorem on Theoretical Physics models

Does Gödel's Second Incompleteness Theorem imply that no Theoretical Physics model of reality can be proved to be consistent using the laws of physics? I work partially in Quantum Information Theory ...
0
votes
0answers
31 views

Quantum mechanics and distribution law in mathematical logics

Recently I've heard that quantum mechanics can be formulated by starting from the rejection of distribution law in mathematical logic: $a$ and $(b$ or $c)$= $(a$ and $b)$ or $(a$ and $c)$. Did ...
1
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2answers
83 views

A question over the reality of $\sin x$

Harmonic functions are in widespread use in physical descriptions of natural real phenomena. I am just wondering therefore how we can define $\sin(x)$ to be part of a real physical quantity (with ...
0
votes
1answer
54 views

Do logarithms appear inside the divergent UV integrals? If so why? [closed]

Do logarithms appear inside the UV divergent integrals of $q\cdot f\cdot t$? I mean expressions of the form of $ \int_{V}d^{r}f(p)log(p^{2}+m^{2}) $ In this case, can we approximate it by $ log(p)= ...
1
vote
1answer
134 views

What kind of math is used in QFT? [duplicate]

What branch(es) of math are used in Quantum Field Theory? Or the question, by way of analogy: Tensor Calculus is to General Relativity as What is to Quantum Field Theory?
-1
votes
2answers
50 views

How would the representation of a circle in 4 dimensions? [closed]

We know that the representation of a square in three dimensions is a cube, and in four dimensions is a tessaract or, hyper cube. With this, How would be the representation of a circle in four ...
2
votes
2answers
112 views

How do you pronounce $\vec{A} \cdot \vec{B}$ and $\vec{A} \times \vec{B}$? [closed]

I'm French. I would like to know: How do you pronounce $\vec{A} \cdot \vec{B}$ : "A scalar B" or "A dot B" ? How do you pronounce $\vec{A} \times \vec{B}$ : "A vectorial B", "A vector B", "A cross ...
6
votes
2answers
120 views

Classical logic in concern with QM Mathematics

In no way am I a physicist, so please excuse improperly used terms. It is in my understanding that Quantum Physics does not obey Classical Logic, hence the existence of Quantum Logic. My questions ...
0
votes
1answer
111 views

What does “projection of a vector” really mean?

Let $\vec{a}$ & $\vec{b}$ be two non-collinear, non-zero co-initial vectors having angle $\theta$ between them. The projection of $\vec{b}$ on $\vec{a}$ is given by the dot product of $\vec{b}$ ...
0
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0answers
22 views

Integration in the three coordinate systems [duplicate]

I need a book teaching triple and double integrations in the three coordinate systems and teaching vectors in three coordinate systems with no in depth mathematics. I need it to help me in general ...
1
vote
0answers
38 views

About category theory and physics [duplicate]

Could the ideas of category theory be applied to Physics, maybe simplifying how algebraic topology and sheaf theory and other hard-to-explain subjects are used in physics?
1
vote
0answers
67 views

Learning Roadmap to Mathematical Physics [duplicate]

Currently, I am a graduate student specializing in algebraic geometry. On the other hand, I have also become extremely interested in the mathematical physics. However, I am not sure what steps I ...
1
vote
1answer
82 views

Proof oriented subjects, similar to computational complexity [closed]

I'm starting my second year as an undergrad math major. I quite like the kind of thought involved in my pure math classes (analysis, abstract algebra), but I also like my physics and (theoretical) ...
0
votes
1answer
117 views

Which textbooks contain info on Bessel functions & their use as basis functions?

As an exercise my research mentor assigned me to solve the following set of equations for the constants $a$, $b$, and $c$ at the bottom. The function $f(r)$ should be a basis function for a ...
2
votes
0answers
164 views

Mathematical Prerequisites for QFT [closed]

I am curious about which areas of mathematics one should be comfortable with before learning QFT. I am familiar with the "learn-it-as-you-go" approach often advocated in physics, but would like to ...
7
votes
2answers
247 views

Mathematical physics text with plenty of applications

I'm looking for texts on mathematical physics. I've seen various other threads, but the texts recommended in those threads were mathematical methods of theoretical physics texts, that is to say those ...
2
votes
0answers
45 views

Mathematical books to become a successful mathematical physicists [duplicate]

My understanding of algebraic topology and Riemannian geometry come from Nakahara's Geometry, Topology, and Physics, which I do not think is sufficient. I am first year PhD student, and I want to do ...
5
votes
4answers
911 views

Intuitive meaning of the exponential form of an unitary operator in Quantum Mechanics

I'm an undergraduate student in Chemistry currently studying quantum mechanics and I have a problem with unitary transformations. Here in my book, it is stated that Every unitary operator ...
0
votes
1answer
61 views

Deviation from 2D trajectory [closed]

I need to find out how far a ball is from the predicted trajectory in 2 dimensional space and I know the start and end position of the ball in both dimensions. Along with that I know the initial ...
0
votes
0answers
37 views

Im a high school finisher and I want to understand Physics theories [duplicate]

I have finished my A Levels (UK high school exam) , and I have studied Further Mathematics, Mathematics, and Physics in high school. I am really interested in learning about theories of Einstein, ...
18
votes
2answers
2k views

What interesting physics problems can't be solved because mathematics is not developed enough? [closed]

I'm curious as to what sorts of physical problems to which we don't have an answer, because we haven't developed the right mathematics yet (or advanced-enough mathematics). Related to this question ...
9
votes
2answers
330 views

If a theory of everything exists, is it necessarily unique?

There is a lot of interesting debate over whether a "theory of everything" (ToE) is allowed to exist in the mathematical sense, see Does Gödel preclude a workable ToE?, Final Theory in Physics: a ...
3
votes
1answer
33 views

Can a Chemical's Opacity be Deduced Mathematically?

all. I have tried Googling but have had no luck. My question is simple (although, I presume the answer is not): If one knows the chemical structure of, well, a chemical, could its optical properties ...
1
vote
0answers
48 views

Translation symmetry and Cauchy products

I often meet the following situation: $$\sum\limits_{n=0} ^\infty \sum\limits_{k=0} ^n f(k)g(n-k)=\sum\limits_{p=0} ^\infty \sum\limits_{q=0}^\infty f(p)g(q)$$ While intuitively this is very clear ...
4
votes
0answers
41 views

Solutions of nonlinear systems invariant wrt. perturbations (looking for applications)

I want to ask if the following purely mathematical problem (that I'm working on) might have some applications to physics. The problem in a nutshell: describe properties of solution sets of real ...
1
vote
0answers
53 views

Study Basic Quantum Mechanics [duplicate]

What is the appropriate mathematical background someone must attain in order to enroll in a quantum physics course for beginners?