相关论文: Quantized Dirac Operators

The goal of this paper is to introduce a class of operators, which we call quantum Dirac type operators on a noncommutative sphere, by a gluing construction from copies of noncommutative disks, subject to an appropriate local boundary…

Recent progress to construct Dirac operators and spinors on compact quantum groups is discussed. The case $SU_q(2)$ is studied carefully and the relationship between known approaches is explained. New examples are given.

Motivated by the recent developments of pseudo-Hermitian quantum mechanics, we analyze the structure generated by unbounded metric operators in a Hilbert space. To that effect, we consider the notions of similarity and quasi-similarity…

Recent advances in the theory of complex symmetric operators are presented and related to current studies in non-hermitian quantum mechanics. The main themes of the survey are: the structure of complex symmetric operators, $C$-selfadjoint…

The magnetic Dirac operator describes the relativistic motion of a charged particle in a magnetic field. Although this operator got a lot of attention in physics many of its fundamental mathematical properties remain unexplored and this…

We develop notions of twisted spinor bundle and twisted pre-quantum bundle on quasi-Hamiltonian G-spaces. The main result of this paper is that we construct a Dirac operator with index given by positive energy representation of loop group.…

The spherically symmetric volume operator is discussed and all its eigenstates and eigenvalues are computed. Even though the operator is more complicated than its homogeneous analog, the spectra are related in the sense that the larger…

We show that the spectral theory of the Dirac operator $D = i\delsl-\sigma(x) -i\pi(x)\gam_5$ in a static background $(\sigma(x),\pi(x))$ in 1+1 space-time dimensions, is underlined by a certain generalization of supersymmetric quantum…

The Pryce (e) spin and position operators of the quantum theory of Dirac's free field were re-defined and studied recently with the help of a new spin symmetry and suitable spectral representations [I. I. Cot\u aescu, Eur. Phys. J. C (2022)…

Gamma matrices for quantum Minkowski spaces are found. The invariance of the corresponding Dirac operator is proven. We introduce momenta for spin 1/2 particles and get (in certain cases) formal solutions of the Dirac equation.

We summarize a recent work on the subject title. The Dirac equation in a curved spacetime depends on a field of coefficients (essentially the Dirac matrices), for which a continuum of different choices are possible. We study the conditions…

A finite dimensional system with a quadratic Hamiltonian constraint is Dirac quantized in holomorphic, antiholomorphic and mixed representations. A unique inner product is found by imposing Hermitian conjugacy relations on an operator…

We investigate examples of quasi-spectral triples over two-dimensional commutative sphere, which are obtained by modifying the order-one condition. We find equivariant quasi-Dirac operators and prove that they are in a topologically…

We set up a framework for discussing `$q$-analogues' of the usual covariant differential operators for hermitian symmetric spaces. This turns out to be directly related to the deformation quantization associated to quadratic algebras…

The role of supercharge operators is studied in the case of a Dirac particle moving in a constant chromomagnetic field. The Hamiltonian is factorised and the ground state wave function in the case of unbroken supersymmetry is determined.

In the high-energy physics literature one finds statements such as ``matrix algebras converge to the sphere''. Earlier I provided a general precise setting for understanding such statements, in which the matrix algebras are viewed as…

By requiring unambiguous symmetric quantization leading to the Dirac equation in a curved space, we obtain a special representation of the spin connections in terms of the Dirac gamma matrices and their space-time derivatives. We also…

The Dirac operator for a manifold Q, and its chirality operator when Q is even dimensional, have a central role in noncommutative geometry. We systematically develop the theory of this operator when Q=G/H, where G and H are compact…

The problem of simulating through quantum walks Dirac fermions in arbitrary curved space-times and coordinates is revisited, taking (1 + 1)D space-times as an example. A new shift or translation operator on the grid is introduced, to take…

The concept of $\mathcal{C}$-symmetries for pseudo-Hermitian Hamiltonians is studied in the Krein space framework. A generalization of $\mathcal{C}$-symmetries is suggested.