Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userMassive conformal particles with non-Abelian charges from free U(2N,2N)-twistor dynamics: quantization and coherent states
123
0
0.0
(
0
)
Authors
M. Calixto
Ask ChatGPT about the research
No Arabic abstract
The inclusion of non-Abelian U(N) internal charges (other than the electric charge) into Twistor Theory is accomplished through the concept of colored twistors (ctwistors for short) transforming under the colored conformal symmetry U(2N,2N). In particular, we are interested in 2N-ctwistors describing colored spinless conformal massive particles with phase space U(2N,2N)/[U(2N)xU(2N)]. Penrose formulas for incidence relations are generalized to N>1. We propose U(2N)-gauge invariant Lagrangians for 2N-ctwistors and we quantize them through a bosonic representation, interpreting quantum states as particle-hole excitations above the ground state. The connection between the corresponding Hilbert (Fock-like with constraints) space and the carrier space of a discrete series representation of U(2N,2N) is established through a coherent space (holomorphic) representation.
rate research
Read More
It is shown that the algebra of diffeomorphism-invariant charges of the Nambu-Goto string cannot be quantized in the framework of canonical quantization. The argument is shown to be independent of the dimension of the underlying Minkowski space.
We revise the use of 8-dimensional conformal, complex (Cartan) domains as a base for the construction of conformally invariant quantum (field) theory, either as phase or configuration spaces. We follow a gauge-invariant Lagrangian approach (of nonlinear sigma-model type) and use a generalized Dirac method for the quantization of constrained systems, which resembles in some aspects the standard approach to quantizing coadjoint orbits of a group G. Physical wave functions, Haar measures, orthonormal basis and reproducing (Bergman) kernels are explicitly calculated in and holomorphic picture in these Cartan domains for both scalar and spinning quantum particles. Similarities and differences with other results in the literature are also discussed and an extension of Schwingers Master Theorem is commented in connection with closure relations. An adaptation of the Borns Reciprocity Principle (BRP) to the conformal relativity, the replacement of space-time by the 8-dimensional conformal domain at short distances and the existence of a maximal acceleration are also put forward.
We classify the finite-dimensional irreducible representations of the Yangians associated with the orthosymplectic Lie superalgebras ${frak{osp}}_{1|2n}$ in terms of the Drinfeld polynomials. The arguments rely on the description of the representations in the particular case $n=1$ obtained in our previous work.
The definitions of para-Grassmann variables and q-oscillator algebras are recalled. Some new properties are given. We then introduce appropriate coherent states as well as their dual states. This allows us to obtain a formula for the trace of a operator expressed as a function of the creation and annihilation operators.
Rarita-Schwinger (RS) quantum free field is reexamined in the context of deformation quantization. It is found out that the subsidiary condition does not introduce any change either in the Wigner function or in other aspects of the deformation quantization formalism, in relation to the Dirac field case. This happens because the vector structure of the RS field imposes constraints on the space of wave function solutions and not on the operator structure. The RS propagator was also calculated within this formalism.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
