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 ...

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What math do I need for mathematical physics? In what manner should I learn math? [closed]

I'm a freshman undergraduate. I've got my sight on mathematical physics. I love math but I don't have the talent nor the inclination for purely abstract mathematics. I also love physics. The only ...
11
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2answers
180 views

Discussions of the axioms of AQFT

The most recent discussion of what axioms one might drop from the Wightman axioms to allow the construction of realistic models that I'm aware of is Streater, Rep. Prog. Phys. 1975 38 771-846, ...
9
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1answer
326 views

Fourier Methods in General Relativity

I am looking for some references which discuss Fourier transform methods in GR. Specifically supposing you have a metric $g_{\mu \nu}(x)$ and its Fourier transform $\tilde{g}_{\mu \nu}(k)$, what does ...
5
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4answers
957 views

Really, how to decide if one can use perturbation theory or not in QM?

In QM, it is said that perturbation theory can be used in case the total Hamiltonian is a sum of 2 parts, one whose exact solution is known and an extra term that contains a small parameter, $\lambda$ ...
6
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1answer
385 views

Thermodynamic limit “vs” the method of steepest descent

Let me use this lecture note as the reference. I would like to know how in the above the expression (14) was obtained from expression (12). In some sense it makes intuitive sense but I would ...
9
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2answers
917 views

Why does iteratively solving the Hartree-Fock equations result in convergence?

[ Cross-posted to the Computational Science Stack Exchange: http://scicomp.stackexchange.com/questions/1297/why-does-iteratively-solving-the-hartree-fock-equations-result-in-convergence ] In the ...
2
votes
2answers
580 views

What is the Hilbert space of a single electron?

Is it the same as the space of all possible descriptions of a single electron? If not, how do they differ? Please give the mathematical name or specification of this space or these spaces.
7
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2answers
644 views

Interesting topics to research in mathematical physics for undergraduates

I'm planning on getting into research in mathematical physics and was wondering about interesting topics I can get into and possibly make some progress on. I'm particularity fond of abstract algebra ...
12
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6answers
1k views

Does the Banach-Tarski paradox contradict our understanding of nature?

Since the Banach-Tarski paradox makes a statement about domains defined in terms of real numbers, it would appear to invalidate statements about nature that we derived by applying real analysis. My ...
7
votes
3answers
2k views

Interesting topics to research in mathematical physics for undergraduates

I'm planning on getting into research in mathematical physics and was wondering about interesting topics I can get into and possibly make some progress on. I'm particularity fond of abstract algebra ...
1
vote
1answer
515 views

Free boundary conditions

I am trying to simulate liquid film evaporation with free boundary conditions (in cartesian coordinates) and my boundary conditions are thus: $$ \frac{\partial h}{\partial x} = 0, \qquad (1) $$ $$ ...
7
votes
2answers
1k 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 ...
5
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3answers
594 views

Axiomatic statistical mechanics

Ive read a few courses on statistical mechanics, and while their textual explanations and example choices differ, the flow of information from microscopy to macroscopy seems the same, and reading ...
5
votes
2answers
384 views

Is there a 1-1 correspondence between symmetry and group theory?

The professor in my class of mathematical physics introduces the definition of groups and said that group theory is the mathematics of symmetry. He gave also some examples of groups such as the set ...
3
votes
1answer
65 views

generation of arbitrary potentials

Suppose you have as many electrically charged particles as needed (even countably many) and consider the open unit ball centered at some point in space. For every continuous real valued function on ...
7
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3answers
1k views

Implications of unbounded operators in quantum mechanics

Quantum mechanical observables of a system are represented by self - adjoint operators in a separable complex Hilbert space $\mathcal{H}$. Now I understand a lot of operators ...
31
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10answers
2k views

Readable books on advanced topics [closed]

I realise that there are already a few questions looking for general book recommendations, but the motivation and type of book I'm looking for here is a little different, so I hope you can indulge me. ...
14
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3answers
1k views

Why can't General Relativity be written in terms of physical variables?

I am aware that the field in General Relativity (the metric, $g_{\mu\nu}$) is not completely physical, as two metrics which are related by a diffeomorphism (~ a change in coordinates) are physically ...
2
votes
2answers
222 views

Why, intuitively, must a solution in physics be unique?

When solving Laplace's equation or Poisson's equation say, we require that the solution must be unique, which can be shown. In general, what is the physics behind seeking a unique solution? Are ...
1
vote
1answer
356 views

A quantum particle in a box (with a catch)

I am reading Shankar's Quantum Mechanics and I am looking at the case where there is one particle inside a box, where the potential is zero inside the wall and abruptly goes to infinity outside the ...
2
votes
1answer
377 views

Is it a total or an explicite time derivative in the Schrödinger equation?

I am always dubious when I need write Schrödinger equation: do I write $\partial / \partial t$ or $d/dt$ ? I suppose it depends on the space in which it is considered. How?
6
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2answers
686 views

What is the symmetry that corresponds to conservation of position?

We know that conserved quantities are associated with certain symmetries. For example conservation of momentum is associated with translational invariance, and conservation of angular momentum is ...
14
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5answers
736 views

Applications of Geometric Topology to Theoretical Physics

Geometric topology is the study of manifolds, maps between manifolds, and embeddings of manifolds in one another. Included in this sub-branch of Pure Mathematics; knot theory, homotopy, manifold ...
5
votes
2answers
113 views

Homogenous vector bundles

In the definition of homogenous vector bundles, an equivalence class is defined. Briefly: G is a lie group and H a (lie) subgroup. Define $$ \rho : H \rightarrow GL(V) $$ where V is a vector ...
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3answers
1k views

Mathematical Physics Book Recommendation [duplicate]

Possible Duplicate: Best books for mathematical background? I want to learn contemporary mathematical physics, so that, for example, I can read Witten's latest paper without checking other ...
8
votes
3answers
138 views

“tmf$(n)$ is the space of supersymmetric conformal field theories of central charge $-n$”

I read this intriguing statement in John Baez' week 197 the other day, and I've been giving it some thought. The post in question is from 2003, so I was wondering if there has been any progress in ...
2
votes
1answer
291 views

Vanishing Ricci flow on a curved manifold

If I understand this right the Ricci flow on a compact manifold given by $\partial g_{\mu \nu} = - 2R_{\mu \nu} + \frac{2}{n}\!R_{\alpha}^{\alpha} \,g_{\mu \nu}$ tends to expand negatively curved ...
2
votes
1answer
114 views

Spinors in more dimensions and new degeneracies?

As you more than probably know spinors dimensions go as $2^{\frac{D}2}$ in D spacetime dimensions. If we look at the peculiar case of D=2*4, spinors have 4 components and we usually say that's related ...
12
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2answers
89 views

Numerical Analysis of Elliptic PDEs

I am looking for an elementary reference regarding issues of stability in numerical analysis of non-linear elliptic PDEs, particularly using the finite difference method (but something more ...
7
votes
1answer
116 views

Simple question on the foundations of spin foam formalism

To make it simple, take the spin foam formalism of ($SU(2)$) 3D gravity. My question is about the choice of the data that will replace the (smoothly defined) fields $e$ (the triad) and $\omega$ (the ...
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10answers
1k views

Examples of number theory showing up in physics

My question is very simple: Are there any interesting examples of number theory showing up unexpectedly in physics? This probably sounds like rather strange question, or rather like one of the ...
3
votes
2answers
163 views

Infinitesimal input, macroscopic output

I must admit that I never got well how physicists handle infinitesimal quantities, mainly because of my education as a mathematician. So the following lines (taken from the preface of Berezin and ...
4
votes
3answers
314 views

Guessing what a simple partial differential equation is describing physically

Is there an easy way to look at a partial different equation and get a sense of what kind of phenomena it is physically describing? I have an equation that looks like this: ...
4
votes
1answer
75 views

Spekkens Toy Model, Internal Comonoids

I have been thinking about Spekkens Toy model in terms of interfaces. The Spekkens paper concerns a physics based on only being able to receive answers to half the number of questions necessary to ...
27
votes
8answers
3k views

Why $\displaystyle i\hbar\frac{\partial}{\partial t}$ can not be considered as the Hamiltonian operator?

In the time dependent Schrodinger equation $\displaystyle, H\Psi = i\hbar\frac{\partial}{\partial t}\Psi$ , the Hamiltonian operator is given by $\displaystyle H = -\frac{\hbar^2}{2m}\nabla^2+V$ ...
12
votes
2answers
155 views

How much of the Capelli-Itzykson-Zuber ADE-classification of su(2)-conformal field theories can one see perturbatively?

In their celebrated work, Capelli Itzykson and Zuber established an ADE-classification of modular invariant CFTs with chiral algebra $\mathfrak{su}(2)_k$. How much of that classification can one ...
5
votes
1answer
106 views

Quantum causal structure

We take causal structure to be some relation defined over elements which are understood to be morphisms of some category. An example of such a relation is a domain, another is a directed acyclic ...
3
votes
2answers
199 views

An integral related to QFT

How to show $$\displaystyle\int\int\int f(p,p')e^{ip\cdot x-ip'\cdot x}d^3pd^3p'd^3x=(2\pi)^3\int f(p,p)d^3p$$ ? I have $p\cdot x=Et-\bf p\cdot x$
2
votes
1answer
326 views

Angular Momentum Operator

I'm looking at a review question I was given and it quite frankly has me stumped. "Using matrix representations find $L^{3}_{x},L^{3}_{y},L^{3}_{z}$ and from these show that $L_{x}, L_{y},L_{z}$ ...
10
votes
2answers
79 views

Examples of heterotic CFTs

I'm trying to get a global idea of the world of conformal field theories. Many authors restrict attention to CFTs where the algebras of left and right movers agree. I'd like to increase my intuition ...
2
votes
2answers
639 views

Taylor approximation in physics

In a textbook about semicoductor physics, I came across a passage about deriving the carrier concentration at thermal equilibrium in semiconductors I didn't quite grasp: The recombination ...
1
vote
1answer
437 views

Differential Equation in Spherical Harmonics Derivation

I've been reviewing derivations of the spherical harmonics in quantum mechanics; mostly as review but also to make sure I understand where the concepts arise from. However, every derivation I've ...
12
votes
4answers
903 views

Rigorous proof of Bohr-Sommerfeld quantization

Bohr-Sommerfeld quantization provides an approximate recipe for recovering the spectrum of a quantum integrable system. Is there a mathematically rigorous explanation why this recipe works? In ...
5
votes
3answers
1k views

canonical and microcanonical ensemble

What does one mean by canonical and micro canonical ensemble in statistical mechanics? Can one elaborate on this in a very simple way with examples? Pardon me, if it is a very simple thing; I am a ...
2
votes
0answers
98 views

Convergence and well-definedness of Lorentzian path integrals

Wick rotation of quantum field theories to Euclidean path integrals with a nonnegative measure everywhere is a wonderful tool. Not so with Lorentzian path integrals. Events far separated in ...
2
votes
1answer
763 views

Simplified partial trace of two operators

If I have two operators A and B living in the Composite Hilbert Space $H_I \bigotimes H_{II} $ and I want to take the partial trace of $C=AB$ over the subspace $H_I$, i.e., $Tr_I[AB]$, is there any ...
10
votes
1answer
402 views

False vacuum in axiomatic QFT

There is an elegant way to define the concept of an unstable particle in axiomatic QFT (let's use the Haag-Kastler axioms for definiteness), namely as complex poles in scattering amplitudes. Stable ...
3
votes
2answers
1k views

Generating Pink Noise

I've generated some white noise in Excel by using the formula $$2*\mathrm{Math.RAND}()-1$$ I would now like to create some pink noise. I believe this is done by applying some sort of filter to the ...
4
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2answers
549 views

Why is the Dirac operator so important - in both physics and mathematics?

Why is the Dirac operator considered so important - in both physics and (pure) mathematics?
9
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1answer
832 views

Quivers in String Theory

Why do a physicist, particularly a string theorist care about Quivers ? Essentially what I'm interested to know is the origin of quivers in string theory and why studying quivers is a natural thing ...