Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userA duality of the classical action yields a reflection symmetry of the quantum energy spectrum
133
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The concept of duality reflects a link between two seemingly different physical objects. An example in quantum mechanics is a situation where the spectra (or their parts) of two Hamiltonians go into each other under a certain transformation. We term this phenomenon as the energy-spectrum reflection symmetry. We develop an approach to this class of problems, based on the global properties of the Riemann surface of the quantum momentum function, a natural quantum-mechanical analogue to the classical momentum. In contrast to the algebraic method, which we also briefly review, our treatment provides an explanation to the long-noticed matching of the perturbative and WKB expansions of dual energy levels. Our technique also reveals the classical origins of duality.
rate research
Read More
Using the fact that the algebra M := M_N(C) of NxN complex matrices can be considered as a reduced quantum plane, and that it is a module algebra for a finite dimensional Hopf algebra quotient H of U_q(sl(2)) when q is a root of unity, we reduce this algebra M of matrices (assuming N odd) into indecomposable modules for H. We also show how the same finite dimensional quantum group acts on the space of generalized differential forms defined as the reduced Wess Zumino complex associated with the algebra M.
The duality symmetry between electricity and magnetism hidden in classical Maxwell equations suggests the existence of dual charges, which have usually been interpreted as magnetic charges and have not been observed in experiments. In quantum electrodynamics (QED), both the electric and magnetic fields have been unified into one gauge field $A_{mu}$, which makes this symmetry inconspicuous. Here, we recheck the duality symmetry of QED by introducing a dual gauge field. Within the framework of gauge-field theory, we show that the electric-magnetic duality symmetry cannot give any new conservation law. By checking charge-charge interaction and specifically the quantum Lorentz force equation, we find that the dual charges are electric charges, not magnetic charges. More importantly, we show that true magnetic charges are not compatible with the gauge-field theory of QED, because the interaction between a magnetic charge and an electric charge can not be mediated by gauge photons.
Let $K$ be a simply connected compact Lie group and $T^{ast}(K)$ its cotangent bundle. We consider the problem of quantization commutes with reduction for the adjoint action of $K$ on $T^{ast}(K).$ We quantize both $T^{ast}(K)$ and the reduced phase space using geometric quantization with half-forms. We then construct a geometrically natural map from the space of invariant elements in the quantization of $T^{ast}(K)$ to the quantization of the reduced phase space. We show that this map is a constant multiple of a unitary map.
235 -
Bozhidar Z. Iliev (Institute for Nuclear Research
, Nuclear Energy
, n Bulgarian Academy of Sciences
2012
The paper recalls and point to the origin of the transformation laws of the components of classical and quantum fields. They are considered from the standard and fibre bundle point of view. The results are applied to the derivation of the Heisenberg relations in quite general setting, in particular, in the fibre bundle approach. All conclusions are illustrated in a case of transformations induced by the Poincare group.
We analyze the behavior of quantum dynamical entropies production from sequences of quantum approximants approaching their (chaotic) classical limit. The model of the quantized hyperbolic automorphisms of the 2-torus is examined in detail and a semi-classical analysis is performed on it using coherent states, fulfilling an appropriate dynamical localization property. Correspondence between quantum dynamical entropies and the Kolmogorov-Sinai invariant is found only over time scales that are logarithmic in the quantization parameter.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
