Applications of algebras in physics are related to the connection of measurable observables to re... more Applications of algebras in physics are related to the connection of measurable observables to relevant elements of the algebras, usually the generators. However, in the determination of the generators in Lie algebras there is place for some arbitrary conventions. The situation is much more involved in the context of quantum algebras, where inside the quantum universal enveloping algebra, we have not enough primitive elements that allow for a privileged set of generators and all basic sets are equivalent. In this paper we discuss how the Drinfeld double structure underlying every simple Lie bialgebra characterizes uniquely a particular basis without any freedom, completing the Cartan program on simple algebras. By means of a perturbative construction, a distinguished deformed basis (we call it the analytical basis) is obtained for every quantum group as the analytical prolongation of the above defined Lie basis of the corresponding Lie bialgebra. It turns out that the whole construc...
In the framework of the canonical quantization of the electromagnetic field, we impose as primary... more In the framework of the canonical quantization of the electromagnetic field, we impose as primary condition on the dynamics the positive definiteness of the energy spectrum. This implies that (Glauber) coherent states have to be considered for the longitudinal and the scalar photon fields. As a result we obtain that the relation holds which in the traditional approach is called the Gupta-Bleuler condition. Gauge invariance emerges as a property of the physical states. The group structure of the theory is recognized to be the one of SU (2)⊗SU (1, 1).
ABSTRACT In a recent paper [Phys. Rev. Lett. 66, 2056 (1991)] the authors have shown how the two ... more ABSTRACT In a recent paper [Phys. Rev. Lett. 66, 2056 (1991)] the authors have shown how the two concepts of quantum groups and squeezing can be bridged in the simple setting provided by a set of states which are a modified version of the states introduced by L. C. Biedenharn and A. J. McFarlane [J. Phys. A, Math. Gen. 22, L873–L878 (1989; Zbl 0708.17015), ibid. 22, 4581-4588 (1989; Zbl 0722.17009)]. They conjecture that the notion of quantum group coherent state is in general the natural candidate to describe squeezed quantum states of matter.
With a simple model of the interaction of two hadrons a critical discussion is given of the veloc... more With a simple model of the interaction of two hadrons a critical discussion is given of the velocity weight function of the thermodynamical model. It is shown that such a function depends on elastic scattering and so lies outside the conventional treatment of thermodynamics. The appearance of a square root divergence at), = 0 is explained, but the model is too simple to reproduce the right elasticity of throughgoing particles and so the velocity function becomes energy dependent and too peaked at low velocities.
Smnmary.-This paper is devoted to the study of angular conditions in the saturation of the chiral... more Smnmary.-This paper is devoted to the study of angular conditions in the saturation of the chiral charge algebra at p~ ~ co within infinite one-particle states. We show that the previously introduced operator u(OZ) cannot suffice to satisfy covarianee oonstraints. The scheme of quarks in a harmonic potential is preserved and a closed but physically unsatisfactory solution is given. Later on, using the whole harmonic-oscillator algebra we present an adiabatic perturbative method which allows us to satisfy angular conditions step by step at any order and overcomes all the difficulties of the first solution. Some phcnomenological considerations are then developed. 1.-Introduction.
A quantitative analysis of the process of condensation of bosons both in harmonic traps and in ga... more A quantitative analysis of the process of condensation of bosons both in harmonic traps and in gases is made resorting to two ingredients only: Bose classical distribution and spectral discretness. It is shown that in order to take properly into account statistical correlations, temperature must be defined from first principles, based on Shannon entropy, and turns out to be equal to $\beta^{-1}$ only for $T > T_c$ where the usual results are recovered. Below $T_c$ a new critical temperature $T_d$ is found, where the specific heat exhibits a sharp spike, similar to the $\lambda$-peak of superfluidity.
We show the presence of non-cyclic phases for oscillating neutrinos in the context of quantum fie... more We show the presence of non-cyclic phases for oscillating neutrinos in the context of quantum field theory. Such phases carry information about the non-perturbative vacuum structure associated with the field mixing. By subtracting the condensate contribution of the flavor vacuum, the previously studied quantum mechanics geometric phase is recovered.
We discuss the gauge structure of real time thermal quantum field theory (thermo field dynamics) ... more We discuss the gauge structure of real time thermal quantum field theory (thermo field dynamics) for dissipative and inhomogeneous systems. We show that a covariant derivative may be conveniently introduced in order to recover the invariance of the lagrangian under space-time-dependent Bogoliubov transformations. In the case of inhomogeneous systems, although we recover canonical commutation relations, the problem of non-locality of the gauge field remains open.
We study algebraic structures underlying 't Hooft's construction relating classical systems with ... more We study algebraic structures underlying 't Hooft's construction relating classical systems with the quantum harmonic oscillator. The role of group contraction is discussed. We propose the use of SU(1, 1) for two reasons: because of the isomorphism between its representation Hilbert space and that of the harmonic oscillator and because zero point energy is implied by the representation structure. Finally, we also comment on the relation between dissipation and quantization.
Generalized quasicoherent states for the Weyl-Heisenberg quantum group have been defined by Biede... more Generalized quasicoherent states for the Weyl-Heisenberg quantum group have been defined by Biedenharn and MacFarlane. In this Letter other quantum Weyl-Heisenberg coherent states are defined for complex q in the usual Fock space. Such states are shown to exhibit interesting squeezing properties, in particular when~q~= 1, for the q analog to the harmonic oscillator.
The Energy Citations Database (ECD) provides access to historical and current research (1948 to t... more The Energy Citations Database (ECD) provides access to historical and current research (1948 to the present) from the Department of Energy (DOE) and predecessor agencies.
The conventional squeezed states of quantum optics, which can be thought of as generalized cohere... more The conventional squeezed states of quantum optics, which can be thought of as generalized coherent states for the algebra SU(1,1), are dynamically generated by single-mode hamiltonians characterized by two-photon process interactions. By the explicit construction of a (highly non-linear) faithful realization of the group [Formula: see text] of automorphisms of SU(1,1), such hamiltonians are shown to be equivalent — up just to elements of [Formula: see text] — to that describing quantum mechanically a damped oscillator.
Quantum pseudo-orthogonal groups SOq(n + 1, n-1) are defined as real forms of quantum orthogonal ... more Quantum pseudo-orthogonal groups SOq(n + 1, n-1) are defined as real forms of quantum orthogonal groups SOq(2n, {2) by means of a suitable antilinear involution. In particular, the case n = 2 gives a quantized Lorentz group.
Applications of algebras in physics are related to the connection of measurable observables to re... more Applications of algebras in physics are related to the connection of measurable observables to relevant elements of the algebras, usually the generators. However, in the determination of the generators in Lie algebras there is place for some arbitrary conventions. The situation is much more involved in the context of quantum algebras, where inside the quantum universal enveloping algebra, we have not enough primitive elements that allow for a privileged set of generators and all basic sets are equivalent. In this paper we discuss how the Drinfeld double structure underlying every simple Lie bialgebra characterizes uniquely a particular basis without any freedom, completing the Cartan program on simple algebras. By means of a perturbative construction, a distinguished deformed basis (we call it the analytical basis) is obtained for every quantum group as the analytical prolongation of the above defined Lie basis of the corresponding Lie bialgebra. It turns out that the whole construc...
In the framework of the canonical quantization of the electromagnetic field, we impose as primary... more In the framework of the canonical quantization of the electromagnetic field, we impose as primary condition on the dynamics the positive definiteness of the energy spectrum. This implies that (Glauber) coherent states have to be considered for the longitudinal and the scalar photon fields. As a result we obtain that the relation holds which in the traditional approach is called the Gupta-Bleuler condition. Gauge invariance emerges as a property of the physical states. The group structure of the theory is recognized to be the one of SU (2)⊗SU (1, 1).
ABSTRACT In a recent paper [Phys. Rev. Lett. 66, 2056 (1991)] the authors have shown how the two ... more ABSTRACT In a recent paper [Phys. Rev. Lett. 66, 2056 (1991)] the authors have shown how the two concepts of quantum groups and squeezing can be bridged in the simple setting provided by a set of states which are a modified version of the states introduced by L. C. Biedenharn and A. J. McFarlane [J. Phys. A, Math. Gen. 22, L873–L878 (1989; Zbl 0708.17015), ibid. 22, 4581-4588 (1989; Zbl 0722.17009)]. They conjecture that the notion of quantum group coherent state is in general the natural candidate to describe squeezed quantum states of matter.
With a simple model of the interaction of two hadrons a critical discussion is given of the veloc... more With a simple model of the interaction of two hadrons a critical discussion is given of the velocity weight function of the thermodynamical model. It is shown that such a function depends on elastic scattering and so lies outside the conventional treatment of thermodynamics. The appearance of a square root divergence at), = 0 is explained, but the model is too simple to reproduce the right elasticity of throughgoing particles and so the velocity function becomes energy dependent and too peaked at low velocities.
Smnmary.-This paper is devoted to the study of angular conditions in the saturation of the chiral... more Smnmary.-This paper is devoted to the study of angular conditions in the saturation of the chiral charge algebra at p~ ~ co within infinite one-particle states. We show that the previously introduced operator u(OZ) cannot suffice to satisfy covarianee oonstraints. The scheme of quarks in a harmonic potential is preserved and a closed but physically unsatisfactory solution is given. Later on, using the whole harmonic-oscillator algebra we present an adiabatic perturbative method which allows us to satisfy angular conditions step by step at any order and overcomes all the difficulties of the first solution. Some phcnomenological considerations are then developed. 1.-Introduction.
A quantitative analysis of the process of condensation of bosons both in harmonic traps and in ga... more A quantitative analysis of the process of condensation of bosons both in harmonic traps and in gases is made resorting to two ingredients only: Bose classical distribution and spectral discretness. It is shown that in order to take properly into account statistical correlations, temperature must be defined from first principles, based on Shannon entropy, and turns out to be equal to $\beta^{-1}$ only for $T > T_c$ where the usual results are recovered. Below $T_c$ a new critical temperature $T_d$ is found, where the specific heat exhibits a sharp spike, similar to the $\lambda$-peak of superfluidity.
We show the presence of non-cyclic phases for oscillating neutrinos in the context of quantum fie... more We show the presence of non-cyclic phases for oscillating neutrinos in the context of quantum field theory. Such phases carry information about the non-perturbative vacuum structure associated with the field mixing. By subtracting the condensate contribution of the flavor vacuum, the previously studied quantum mechanics geometric phase is recovered.
We discuss the gauge structure of real time thermal quantum field theory (thermo field dynamics) ... more We discuss the gauge structure of real time thermal quantum field theory (thermo field dynamics) for dissipative and inhomogeneous systems. We show that a covariant derivative may be conveniently introduced in order to recover the invariance of the lagrangian under space-time-dependent Bogoliubov transformations. In the case of inhomogeneous systems, although we recover canonical commutation relations, the problem of non-locality of the gauge field remains open.
We study algebraic structures underlying 't Hooft's construction relating classical systems with ... more We study algebraic structures underlying 't Hooft's construction relating classical systems with the quantum harmonic oscillator. The role of group contraction is discussed. We propose the use of SU(1, 1) for two reasons: because of the isomorphism between its representation Hilbert space and that of the harmonic oscillator and because zero point energy is implied by the representation structure. Finally, we also comment on the relation between dissipation and quantization.
Generalized quasicoherent states for the Weyl-Heisenberg quantum group have been defined by Biede... more Generalized quasicoherent states for the Weyl-Heisenberg quantum group have been defined by Biedenharn and MacFarlane. In this Letter other quantum Weyl-Heisenberg coherent states are defined for complex q in the usual Fock space. Such states are shown to exhibit interesting squeezing properties, in particular when~q~= 1, for the q analog to the harmonic oscillator.
The Energy Citations Database (ECD) provides access to historical and current research (1948 to t... more The Energy Citations Database (ECD) provides access to historical and current research (1948 to the present) from the Department of Energy (DOE) and predecessor agencies.
The conventional squeezed states of quantum optics, which can be thought of as generalized cohere... more The conventional squeezed states of quantum optics, which can be thought of as generalized coherent states for the algebra SU(1,1), are dynamically generated by single-mode hamiltonians characterized by two-photon process interactions. By the explicit construction of a (highly non-linear) faithful realization of the group [Formula: see text] of automorphisms of SU(1,1), such hamiltonians are shown to be equivalent — up just to elements of [Formula: see text] — to that describing quantum mechanically a damped oscillator.
Quantum pseudo-orthogonal groups SOq(n + 1, n-1) are defined as real forms of quantum orthogonal ... more Quantum pseudo-orthogonal groups SOq(n + 1, n-1) are defined as real forms of quantum orthogonal groups SOq(2n, {2) by means of a suitable antilinear involution. In particular, the case n = 2 gives a quantized Lorentz group.
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Papers by E. Celeghini