Tagged Questions
-2
votes
0answers
21 views
Place in Europe where there are research groups with anti-de-Sitter geometry or minimal Lagrangian mappings [closed]
I am not sure whether this question is appropriate for this forum, but I am a mathematician with Ph.D. looking to apply to physics departments in Europe as a postdoctoral researcher where there are ...
1
vote
0answers
35 views
Ascertaining a mathematical equality to derive a partition function
we have an equation like this:
$$\mathcal N(x)=\sum_{q=1}^\infty (\psi(x,q) \log(q)) \qquad (1)$$
while $\psi(x)$ is the function for some oscillations (may contain complex part), $x\in \Bbb R$ and ...
1
vote
0answers
40 views
Applications of a certain wave equation in Physics? [closed]
I am doing research in the field of number theory and as part of this looking for correspondencies to other discilines and particularly physics.
I am searching for examples in physics where the ...
7
votes
6answers
260 views
In coordinate-free relativity, how do we define a vector?
Relativity can be developed without coordinates: Laurent 1994 (SR), Winitzski 2007 (GR).
I would normally define a vector by its transformation properties: it's something whose components change ...
0
votes
1answer
93 views
Spin(n) group SO(n) relation
Is it correct to state that the elements of Spin(n) fulfill a Clifford algebra and that the Lie group generators of Spin(n) is given by the commutator of the elements?
If not, then what is the ...
5
votes
3answers
244 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 ...
1
vote
2answers
182 views
How much pure math should a physics/microelectronics person know [duplicate]
I do condensed matter physics modeling in my phd and I was struck up learning quite an amount of physics. But while having done lot of physics courses, I see that if I learn pure math I would ...
1
vote
1answer
110 views
Topology for physicists [duplicate]
Which are the best introductory books for topology, algebraic geometry, manifolds etc, needed for string theory?
2
votes
0answers
203 views
Interesting Math Topics Useful for Physics [closed]
What are some interesting, but less popular, math topics that are useful for physics that can be self-studied? Specifically, topics that might ultimately be useful in high energy theory (even if it is ...
7
votes
2answers
426 views
How should a theoretical physicist study maths? [duplicate]
Possible Duplicate:
How should a physics student study mathematics?
If some-one wants to do research in string theory for example, Would the Nakahara Topology, geometry and physics book and ...
2
votes
2answers
269 views
(Co)homology of the universe
In this post let $U$ be the universe considered as a manifold.
From what I gather we don't really have any firm evidence whether the universe is closed or open. The evidence seems to point towards it ...
6
votes
5answers
429 views
Is physics rigorous in the mathematical sense?
I am a student studying Mathematics with no prior knowledge of Physics whatsoever except for very simple equations. I would like to ask, due to my experience with Mathematics:
Is there a set of ...
10
votes
3answers
354 views
Does the axiom of choice appear to be “true” in the context of physics?
I have been wondering about the axiom of choice and how it relates to physics. In particular, I was wondering how many (if any) experimentally-verified physical theories require axiom of choice (or ...
4
votes
1answer
138 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 ...
5
votes
1answer
287 views
Reference for mathematics of string theory [closed]
I have a great interest in the area of string theory, but since I am more focused on mathematics, I was wondering if there is any book out there that covers mathematical aspects of string theory. I ...
3
votes
1answer
227 views
Mathematical definitions in string theory
Does anyone know of a book that has mathematical definitions of a string, a $p$-brane, a $D$-brane and other related topics. All the books I have looked at don't have a precise definition and this is ...
4
votes
2answers
131 views
Quantum Mechanics in terms of *-algebras
I'm currently trying to find my way into the geometric description of Quantum Mechanics. I therefor started reading:
Geometry of state spaces. In: Entanglement and Decoherence (A. Buchleitner et ...
3
votes
5answers
328 views
What is the meaning of following expresion $C=\frac{\delta Q}{dT}$ mathematicly
Our professor raised the following question during our lecture in Statistical Physics (even so it's related to Thermodynamics):
Many text books (even wikipedia) writes wrong expressions (from ...
6
votes
2answers
190 views
Quantum mechanics on Cantor set?
Has quantum mechanics been studied on highly singular and/or discrete spaces? The particular space that I have in mind is (usual) Cantor set. What is the right way to formulate QM of a particle on a ...
0
votes
0answers
54 views
Is it possible to use the properties of quantum mechnics to develop a computer that develop mathmatical theory? [closed]
Is it possible to use the properties of quantum mechnics to develop a computer that develop mathmatical theory?
I want some reference please, because i want to get into very detailed.
Thanks in ...
1
vote
0answers
120 views
How is the poincare conjecture(and perelman proof) helpful in studying the properties of the universe?
Can someone tell me how the poincare's famous conjecture or its proof by perelmen can be helpful in deciding some properties like the shape of the universe?
3
votes
4answers
486 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 ...
4
votes
2answers
374 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 ...
2
votes
0answers
135 views
What are the topics of string theory that are comprehensible with only a mathematical background on Manifolds and Algebraic Topology?
What are the topics of string theory that are comprehensible with only a mathematical background on manifolds and algebraic topology? Also, I have read only the first four chapters in Peskin & ...
3
votes
1answer
227 views
How do I find the tensor components of all weights of a representation of SU(3), e.g. the six dimensional representation (2,0)
How do I find the corresponding tensor component v^ij of the six dimensional representation of SU(3) with dynkin label (2,0).
7
votes
2answers
209 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 ...
7
votes
2answers
737 views
A book on quantum mechanics supported by the high-level mathematics
I'm interested in quantum mechanics book that uses high level mathematics (not only the usual functional analysis and the theory of generalised functions but the theory of pseudodifferential operators ...
1
vote
1answer
319 views
Bra space and adjoint vectors
If I'm not wrong, a bra, $ \langle \phi_n | $, can be thought as a linear functional that when applied to a ket vector, $| \phi_m \rangle$, returns a complex number; that is, the inner product it's a ...
5
votes
3answers
1k views
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 ...
26
votes
10answers
692 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.
...
0
votes
0answers
131 views
Journals on mathematics similar to the American Journal of Physics and the Physics Teacher [closed]
For the moderators: Please feel free to transfer this question to math.stackexchange if you find that it does not fit physics.stackexchange.
It is known that American Journal of Physics and the ...
23
votes
9answers
584 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
131 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 ...
3
votes
2answers
172 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
169 views
What determine whether the dynamical equations are tensor equations or vector equations?
Newton's 2nd law which is central to Newtonian dynamics, is a vector equation
$\sum\textbf{F}_{external}=m\textbf{a}$
Same with Maxwell's equations in the covariant form.
On the other hand, ...
7
votes
8answers
591 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 ...
33
votes
18answers
2k views
Quantum Field Theory from a mathematical point of view
I'm a student of mathematics with not much background in physics. I'm interested in learning Quantum field theory from a mathematical point of view.
Are there any good books or other reference ...
38
votes
6answers
831 views
The Role of Rigor
The purpose of this question is to ask about the role of mathematical rigor in physics. In order to formulate a question that can be answered, and not just discussed, I divided this large issue into ...
9
votes
2answers
475 views
Transforming a sum into an integral
I posted this in the mathematical forums. Maybe you will help me. I found an hard article http://prola.aps.org/abstract/PR/v105/i3/p776_1 of yang huang and luttinger. The authors begins with the sum: ...
2
votes
4answers
451 views
Generalized functions in physics
Prior to the Dirac delta function, what other distributions functions where physicists using? I find it hard to motivate the theory of generalized functions with just the delta function alone.
4
votes
2answers
255 views
Combinatorial sum in a problem with a Fermi gas
I'm solving a problem involving a Fermi gas. There is a specific sum I cannot figure my way around.
A set of equidistant levels, indexed by $m=0,1,2 \ldots$, is populated by spinless fermions with ...
2
votes
6answers
2k views
real world applications of Mathematics which use functions with singularities, not just as a matter of mathematical taste but for conceptual reasons
EDIT [for aptness of this question to this site, read 'real world applications' as 'applications in Physics']
The concept of function (of the form $f : \mathbb{R} \to \mathbb{R}$ ) has been used in ...
2
votes
2answers
309 views
How do you find conserved quantities for linear second order ODEs?
I have a differential equation of the form
$ \frac{d^2 y}{dt^2} + f(t) \frac{dy}{dt} + g(t) y = 0 $
where $f$ and $g$ are known functions of time.
Is there a systematic (or otherwise) way of ...
2
votes
2answers
269 views
a question on Lagrange's equation when the time derivative of the generalized co-ordinates is constant
Consider a system whose generalized co-ordinates are $q_i$ and is under the constraints $\dot{q_i} = K_i \forall i = 1,2,3,...$ where $K_i$ are constants. I have a problem in writing the Lagrange's ...
2
votes
2answers
487 views
Helmholtz decomposition in the plane
Prove or disprove the following proposition:
For any smooth plane vector field $\mathbf{H}=\left(H_x,H_y\right)$, there exist scalar potentials $\phi$, $\psi$ such that
$H_x=\frac{\partial \phi ...
4
votes
1answer
1k views
Uniqueness of Helmholtz decomposition?
Helmholtz theorem states that given a smooth vector field $\pmb{H}$, there are a scalar field $\phi$ and a vector field $\pmb{G}$ such that
$$\pmb{H}=\pmb{\nabla} \phi +\pmb{\nabla} \times \pmb{G},$$
...
0
votes
1answer
168 views
A question on smooth 1-manifolds
Consider two people living on two different smooth 1-manifolds $S$ and $T$ as shown in figure 1. The manifold $S$ is a bump function joining the points $A$ and $B$ and the manifold $T$ is formed by ...
3
votes
1answer
1k views
Why is the Yang–Mills existence and mass gap problem so fundamental?
Ref: Yang–Mills existence and mass gap
Can anyone please explain why the Yang–Mills Existence and Mass Gap problem is so important / fundamental to contemporary mathematics (and, presumably, ...
2
votes
4answers
2k views
How many digits of Pi are required in physics?
In other words: which physics experiment requires to know Pi with the highest precision?
10
votes
2answers
903 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 ...
