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        Mathematical methods in classical mechanics, classical and quantum field theory, quantum mechanics, statistical mechanics, condensed matter, nuclear and atomic physics.

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        332 views

        Harmonic oscillator in spherical coordinates

        It is probably the most well-known result in quantum mechanics that the harmonic oscillator can be solved by supersymmetry. More precisely, the operator $$-\frac{d^2}{dx^2}+x^2$$ can be ...
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        vote
        0answers
        81 views

        Holomorphic map, Instantons of Complex Projective Space and Loop Group

        It seems that holomorphic (or rational) maps play a crucial role to relate the following data: Instanton in 1-dimensional complex Projective Space $$\mathbb{P}^1$$ in a 2 dimensional (2d) spacetime. ...
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        votes
        0answers
        108 views

        Chern-Simons theory with non-compact gauge groups G

        This is related to a previous question, where a nonlinear σ model (NLSM) describes a scalar field Σ which takes on values in a nonlinear manifold called the target manifold T. There we ask the general ...
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        votes
        0answers
        99 views

        Minkowski isometries

        Consider theorem 1.7 from chapter III of 'Elementary differential geometry' by O'Neill. It says that: Theorem 1.7: If $\phi$ is an isometry of $E^3 $, then there exists a unique translation $T$ and a ...
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        votes
        1answer
        301 views

        Does current follow the path(s) of least (total) resistance?

        Consider Poisson equation $\nabla \cdot (\sigma(x)\nabla u)=0$ in a domain $D$, where $\sigma(x)$ is the spatially dependent conductivity. On the boundary we have $2$ electrodes $E_1$ and $E_2$ (...
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        votes
        0answers
        227 views

        Witten zeta function v.s. Riemann zeta function

        From a talk, we learned that The symplectic volume of the space $M$ of gauge equivalence classes of flat G connections is given by the “Witten zeta function”: where we sum over irreducible ...
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        votes
        1answer
        103 views

        Nonlinear sigma models with non-compact groups / target spaces

        A nonlinear σ model (NLSM) describes a scalar field Σ which takes on values in a nonlinear manifold called the target manifold T. The target manifold T is equipped with a Riemannian metric g. Σ is ...
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        votes
        0answers
        105 views

        Conserved Positive Charge for a PDE

        Let $(x,t) \in \mathbb{R}^2$ and consider the following partial differential equation for the real-valued function $U(x,t)$: \begin{equation} \frac{\partial^2 U}{\partial t^2} = - \frac{\hbar^2}{4m^2} ...
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        votes
        1answer
        208 views

        Moduli space of flat connections over a Riemann surface

        If I understand correctly, in the Refs below: We can see that the moduli space of SU($N$) flat connections over a torus, is equivalent to a complex projective space $\mathbb{P}^{N-1}$ Namely, $$ M_{\...
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        votes
        1answer
        72 views

        Reference request for quantum Teichmuller space

        I would like to ask for some detailed reference for quantum Teichmuller theory, better in a mathematical taste. I read a little bit on Kashaev's or Chekhov and Fock's, but find that I need to fill ...
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        votes
        1answer
        229 views

        The Precise Meaning of the Moduli Space of Flat Connections?

        Questions: I would like to have a precise description of the meanings of the Moduli Space of Flat Connections, such that it is understandable by mathematical physicists and physicists. For 3d Chern-...
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        vote
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        88 views

        Solution of nonlinear heat equation decreases in time

        Let $f\colon \mathbb{R} \to \mathbb{R}$ be a smooth decreasing function which is non-negative and bounded above, and consider the heat equation on a smooth bounded domain $$u_t - \Delta u = f(u)$$ ...
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        0answers
        91 views

        Coleman–Mandula theorem and a mathematical proof

        Coleman–Mandula theorem (by Sidney Coleman and Jeffrey Mandula) [1] is a no-go theorem in theoretical physics. It states that "space-time and internal symmetries cannot be combined in any but a ...
        1
        vote
        1answer
        66 views

        stationary measure for linear cocycle(random transformation matrices)

        Let $(M,\mathcal B, \mu)$ be a probability space which $M=\{A_{1},A_{2},...,A_{N}\}^{\mathbb{N}}$ ($A_{i} \in GL(d ,\mathbb{R})$) and $\mu=p^{\mathbb{N}}$. Let $F:M\times \mathbb R^d\to M\times \...
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        votes
        1answer
        84 views

        Further Developments of Lieb-Schultz-Mattis theorem in Mathematics

        The Lieb-Schultz-Mattis theorem [1] and its higher-dimensional generalizations [2] says that a translation-invariant lattice model of spin-1/2's cannot allow a non-degenerate ground state preserving ...

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        山西福彩快乐十分钟
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