Thick morphisms of supermanifolds, quantum mechanics, and spinor representation

  title={Thick morphisms of supermanifolds, quantum mechanics, and spinor representation},
  author={Hovhannes M. Khudaverdian and Theodore Th. Voronov},
  journal={Journal of Geometry and Physics},
Quantization of (-1)-Shifted Derived Poisson Manifolds
. We inv estigate the quantization problem of ( − 1) -shifted derived Poisson manifolds in terms of BV ∞ -operators on the space of Berezinian half-densities. We prove that quantizing such a ( − 1)
Symplectic microgeometry, IV: Quantization
We construct a special class of semiclassical Fourier integral operators whose wave fronts are symplectic micromorphisms. These operators have very good properties: they form a category on which the
Frame covariant formalism for fermionic theories
We present a frame- and reparametrisation-invariant formalism for quantum field theories that include fermionic degrees of freedom. We achieve this using methods of field-space covariance and the
Non-linear homomorphisms of algebras of functions are induced by thick morphisms.
In 2014, Voronov introduced the notion of thick morphisms of (super)manifolds as a tool for constructing $L_{\infty}$-morphisms of homotopy Poisson algebras. Thick morphisms generalise ordinary


Thick morphisms of supermanifolds and oscillatory integral operators
We show that thick morphisms (or microformal morphisms) between smooth (super)manifolds, introduced by us before, are classical limits of 'quantum thick morphisms' defined here as particular
Graded Geometry, Q‐Manifolds, and Microformal Geometry
We give an exposition of graded and microformal geometry, and the language of Q‐manifolds. Q‐manifolds are supermanifolds endowed with an odd vector field of square zero. They can be seen as a
Berezinians, Exterior Powers and Recurrent Sequences
We study power expansions of the characteristic function of a linear operator A in a p|q-dimensional superspace V. We show that traces of exterior powers of A satisfy universal recurrence relations
Categories of Symmetries and Infinite-Dimensional Groups
Preface 1. Visible and invisible structures on infinite-dimensional groups 2. Spinor representation 3. Representations of the complex classical categories 4. Fermion Fock space 5. The Weil
The Schrödinger Equation
1. General Concepts of Quantum Mechanics.- 1.1. Formulation of Basic Postulates.- 1.2. Some Corollaries of the Basic Postulates.- 1.3. Time Differentiation of Observables.- 1.4. Quantization.- 1.5.
Fourier integral operators. I
Pseudo-differential operators have been developed as a tool for the study of elliptic differential equations. Suitably extended versions are also applicable to hypoelliptic equations, but their value
On the canonical transformation in classical and quantum mechanics
A more exact formulation for Dirac’s proposition on the analogy between the unitary transformations in quantum theory and the contact transformations in classical theory is given. It is shown that
: This work presents a novel zero in-plane Poisson’s ratio honeycomb design for large out-of-plane deformations and morphing. The novel honeycomb topology is composed by two parts that provide