A generalization of the Bogoliubov transformation is developed to describe a space compactified fermionic field. The method is the fermionic counterpart of the formalism introduced earlier for bosons ...Phys. Rev. A 66 (2002) 052101, and is based on the thermofield dynamics approach. We analyze the energy–momentum tensor for the Casimir effect of a free massless fermion field in a
d-dimensional box at finite temperature. As a particular case the Casimir energy and pressure for the field confined in a three-dimensional parallelepiped box are calculated. It is found that the attractive or repulsive nature of the Casimir pressure on opposite faces changes depending on the relative magnitude of the edges. We also determine the temperature at which the Casimir pressure in a cubic box changes sign and estimate its value when the edge of the cube is of the order of the confining lengths for baryons.
The book is directed to researchers and graduate students pursuing an advanced degree. It provides details of techniques directed towards solving problems in non-linear dynamics and chos that are, in ...general, not amenable to a perturbative treatment. The consideration of fundamental interactions is a prime example where non-perturbative techniques are needed. Extension of these techniques to finite temperature problems is considered. At present these ideas are primarily used in a perturbative context. However, non-perturbative techniques have been considered in some specific cases. Experts in the field on non-linear dynamics and chaos and fundamental interactions elaborate the techniques and provide a critical look at the present status and explore future directions that may be fruitful. The text of the main talks will be very useful to young graduate students who are starting their studies in these areas.
The Galilean-invariant field theories are quantized by using the canonical method and the five-dimensional Lorentz-like covariant expressions of non-relativistic field equations. This method is ...motivated by the fact that the extended Galilei group in 3
+
1 dimensions is a subgroup of the inhomogeneous Lorentz group in 4
+
1 dimensions. First, we consider complex scalar fields, where the Schrödinger field follows from a reduction of the Klein–Gordon equation in the extended space. The underlying discrete symmetries are discussed, and we calculate the scattering cross-sections for the Coulomb interaction and for the self-interacting term
λΦ
4. Then, we turn to the Dirac equation, which, upon dimensional reduction, leads to the Lévy-Leblond equations. Like its relativistic analogue, the model allows for the existence of antiparticles. Scattering amplitudes and cross-sections are calculated for the Coulomb interaction, the electron–electron and the electron–positron scattering. These examples show that the so-called ‘non-relativistic’ approximations, obtained in low-velocity limits, must be treated with great care to be Galilei-invariant. The non-relativistic Proca field is discussed briefly.
Considering basic ingredients of the so-called thermofield dynamics associated with a Lie algebra,
L
, an algebra,
L
T, is derived using the first kind of solution of the modified Yang-Baxter ...equation.
L
T has a double algebraic structure and represents a new possibility of representations for Lie symmetries associated with the thermal phenomena. As an example, the Poincaré group is studied.
In this work, the Ginzburg-Landau theory is represented on a symplectic manifold with a phase space content. The order parameter is defined by a quasi-probability amplitude, which gives rise to a ...quasi-probability distribution function, i.e., a Wigner-type function. The starting point is the thermal group representation of Euclidean symmetries and gauge symmetry. Well-known basic results on the behavior of a superconductor are re-derived, providing the consistency of representation. The critical superconducting current density is determined and its usual behavior is inferred. The negativety factor associated with the quasi-distribution function is analyzed, providing information about the non-classicality nature of the superconductor state in the region closest to the edge of the superconducting material.
The Lake Louise Winter Institute is held annually to explore recent trends in physics. Pedagogical and review lectures are presented by invited experts. A topical workshop is held in conjunction with ...the Institute, with contributed presentations by participants.
A representation theory for Lie groups is developed taking the Hilbert space, say
H
w
, of the
w
∗
-algebra standard representation as the representation space. In this context the states describing ...physical systems are amplitude wave functions but closely connected with the notion of the density matrix. Then, based on symmetry properties, a general physical interpretation for the dual variables of thermal theories, in particular the thermofield dynamics (TFD) formalism, is introduced. The kinematic symmetries, Galilei and Poincaré, are studied and (density) amplitude matrix equations are derived for both of these cases. In the same context of group theory, the notion of phase space in quantum theory is analysed. Thus, in the non-relativistic situation, the concept of density amplitude is introduced, and as an example, a spin-half system is algebraically studied; Wigner function representations for the amplitude density matrices are derived and the connection of TFD and the usual Wigner-function methods are analysed. For the Poincaré symmetries the relativistic density matrix equations are studied for the scalar and spinorial fields. The relativistic phase space is built following the lines of the non-relativistic case. So, for the scalar field, the kinetic theory is introduced via the Klein–Gordon density-matrix equation, and a derivation of the Jüttiner distribution is presented as an example, thus making it possible to compare with the standard approaches. The analysis of the phase space for the Dirac field is carried out in connection with the dual spinor structure induced by the Dirac-field density-matrix equation, with the physical content relying on the symmetry groups. Gauge invariance is considered and, as a basic result, it is shown that the Heinz density operator (which has been used to develope a gauge covariant kinetic theory) is a particular solution for the (Klein–Gordon and Dirac) density-matrix equation.
We report mutations in the gene for
topoisomerase I–binding
RS protein (
TOPORS) in patients with autosomal dominant retinitis pigmentosa (adRP) linked to chromosome 9p21.1 (locus
RP31). A ...positional-cloning approach, together with the use of bioinformatics, identified
TOPORS (comprising three exons and encoding a protein of 1,045 aa) as the gene responsible for adRP. Mutations that include an insertion and a deletion have been identified in two adRP-affected families—one French Canadian and one German family, respectively. Interestingly, a distinct phenotype is noted at the earlier stages of the disease, with an unusual perivascular cuff of retinal pigment epithelium atrophy, which was found surrounding the superior and inferior arcades in the retina. TOPORS is a RING domain–containing E3 ubiquitin ligase and localizes in the nucleus in speckled loci that are associated with promyelocytic leukemia bodies. The ubiquitous nature of TOPORS expression and a lack of mutant protein in patients are highly suggestive of haploinsufficiency, rather than a dominant negative effect, as the molecular mechanism of the disease and make rescue of the clinical phenotype amenable to somatic gene therapy.
Quantum chaos in the finite-temperature Yang-Mills-Higgs system is studied. The energy spectrum of a spatially homogeneous SU(2) Yang-Mills-Higgs system is calculated within thermofield dynamics. ...Level statistics of the spectra is studied by plotting nearest-level spacing distribution histograms. It is found that finite-temperature effects lead to a strengthening of chaotic effects, i.e. a spectrum which has the Poissonian distribution at zero temperature has the Gaussian distribution at finite temperature.
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