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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72 views

Any other mathematical fields in physics than $\mathbb{R}$ or $\mathbb{C}$? [on hold]

In physics, we usually use the real number field $\mathbb{R}$ or the complex number field $\mathbb{C}$. Does any other field find use in physics too?
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2answers
87 views

Reference for mathematics of statistical mechanics

I'm looking for materials (books, articles, etc) which focus ONLY on the mathematics of statistical mechanics (as I have no background in physics). The materials may have some simple explanations or ...
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1answer
43 views

Is it physics that leads to development of maths or is it maths that leads to the development of physics? [on hold]

Like calculus(which is maths) was discovered from physics. Are there theories in which maths leads to the discovery of new physics theories? So is it physics that lead to development of maths or its ...
2
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1answer
107 views

Why Newton wanted lines to be generated by continued motion of points rather than by apposition of parts?

The following passage has been extracted from the Newton's (John Stewart's English translated version) "Sir Issac Newton's two Treatises: Of the Quadrature of Curves, and Analysis by equations of an ...
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1answer
26 views

Formula relating sum of values of a function to its integral

I came across the above formula in some quantum mechanics lecture notes explaining the Casimir effect. Anyone seen it before if so could you please tell me its 'name'. B refers to the Bernoulli ...
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5answers
653 views

What does it mean for a physical quantity if its mixed second partial derivatives are not equal?

This goes for every problem (either in electromagnetism or fluid dynamics) that has to do with vector fields. Say we have a fluid flowing in a closed circular pipe (or an electromagnetic field, the ...
4
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2answers
46 views

Pointwise and uniform convergence. Examples from physics

I am a first-year mathematical student, and from a mathematical perspective I understand the difference between pointwise and uniform convergence of sequences and series of functions. However, I have ...
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0answers
31 views

Aplications of algebraic topology/pure mathematics in nuclear fusion

I am planning on working on an independent research class this fall at a community college. My instructor wants to focus it around pure mathematics/topology/homotopy. I think she has done a phd in ...
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0answers
33 views

Subject is Maths that would complement Physics? [closed]

Suppose Math has 5 sub parts- Analysis: Analysis, Complex Analysis, Measure theory and integration,Functional Analysis Algebra: Group Theory, Vectors space-rings-modules, Galois, Algebra Number ...
2
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2answers
97 views

Mathematics needed for string theory [duplicate]

I'm interested in cutting edge string theory studied by research physicist. I'm wonder what mathematics is needed and how far am I in terms of mathematics background needed and how much more ...
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3answers
102 views

Can pure mathematics alone give proofs in science [closed]

I reasoned in my last post that because of science's nature of induction and falsifiability, it is impossible to give a theorem in science, unlike in mathematics. It is because even when a scientific ...
0
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1answer
73 views

Numerically summing a divergent series [duplicate]

Say I have a closed form expression for a divergent series and I can calculate as many terms in it as I want. What options have I got to obtain a meaningful result for this divergent series?
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1answer
53 views

Trajectories piecewise smooth?

In my studies of calculus and real analysis I have found the proofs of several theorems, commonly used in physics, such as those concerning the conservativity of fields, for example like If ...
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0answers
38 views

Dirac delta function equation intuition and proof [duplicate]

What is the intuition and where should I find proof of this equation (do not know what its name is). It is used to derive Gauss law from Newton equation. $${\nabla \cdot \Bigg ( ...
6
votes
5answers
640 views

Is it possible to have infinite combinations in reality?

On a yoghurt advert, the voiceover claimed that you have infinite combinations with it. However, given that there is a finite amount of matter, is it possible to have infinite combinations with the ...
2
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0answers
58 views

Convert discrete sum to principal integral

I'm studying IQHE beginning with Laughlin's famous gauge argument. I referred to his Nobel Lecture, in which he mentioned a paper that enlightened him. It is Phys.Rev.B.23.5632(1981) which talked ...
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0answers
54 views

Is it possible to express continuous growth without using transcendental numbers? [closed]

Continuous growth is typically expressed using some variant on $A = Pe^{rt}$, I understand where $e$ comes from in general, it is the amount something grows in a given time interval, when continuously ...
3
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1answer
82 views

What really are perturbation expansions?

I'm unsure if this question belongs here or at Math.SE, but since I've got to it by reading some articles about Physics I'm going to post it here anyway. In this particular article (Theoretical ...
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1answer
37 views

Calculating average quantities in kinetic theory

Consider a volume $V$ with $5$ particles each of mass $m$ at positions $\mathbf{q}_i=(x_i,y_i,z_i) \in V$ and with velocities $\mathbf{v}_i=(u_i,v_i,w_i)$. The speeds of the particles are between $0$ ...
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0answers
12 views

Poisson bracket in 4d phase space

In phase space determined by $(q_i,p_i)$ the Poisson bracket of two functions f and g is $$\{f,g\}=\sum_{i=1}^N\frac{\partial f}{\partial q_i}\frac{\partial g}{\partial p_i}-\frac{\partial g}{\partial ...
1
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1answer
56 views

The grand partition function of non interacting hamiltonians

In the case of non interacting particles I know we can write the Hamiltonian as $$H(\mathbf{q}_1,\dots,\mathbf{p}_1,\dots)=\sum_{i=1}^N h(\mathbf{q}_i,\mathbf{p}_i)$$ but I am having trouble ...
1
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2answers
195 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 ...
2
votes
2answers
64 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 ...
3
votes
1answer
296 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 ...
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1answer
98 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 ...
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1answer
61 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
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1answer
66 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?
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4answers
78 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 ...
13
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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 ...
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0answers
58 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
104 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 ...
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0answers
40 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
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2answers
68 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
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1answer
74 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 ...
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0answers
38 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
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1answer
46 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
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0answers
56 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
464 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
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2answers
156 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
132 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
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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 ...
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0answers
45 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
122 views

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

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
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0answers
33 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 ...
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2answers
86 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
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1answer
56 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
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1answer
164 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?
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2answers
86 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
123 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
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2answers
152 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 ...