117996890
Four-potentials and Maxwell Field Tensors from $SL(2,C)$ Spinors as Infinite-Momentum/Zero-Mass Limits of their Massive Counterparts
Four $SL(2,C)$ spinors are considered within the framework of Wigner's little groups which dictate internal space-time symmetries of relativistic particles. It is indicated that the little group for a massive particle at rest is $O(3)$, while it is $O(3)$-like for a moving massive particle. The little group becomes like $E(2)$ in the infinite-momentum/zero-mass limit. Spin-$\frac{1}{2}$ particles are studied in detail, and the origin of the gauge degrees of freedom for massless particles is clarified. There are sixteen different combinations of direct products of two $SL(2,C)$ spinors for spin-1 and spin-0 particles. The state vectors for the $O(3)$ and $O(3)$-like little groups are constructed. It is shown that in the infinite-momentum/zero-mass limit, these state vectors become scalars, four-potentials and the Maxwell field tensor. It is revealed that the Maxwell field tensor so obtained corresponds to some of the state vectors constructed by Weinberg in 1964.
1673726
Symmetries Shared by the Poincaré Group and the Poincaré Sphere
Henri Poincare formulated the mathematics of Lorentz transformations, known as the Poincare group. He also formulated the Poincare sphere for polarization optics. It is shown that these two mathematical instruments can be derived from the two-by-two representations of the Lorentz group. Wigner’s little groups for internal space-time symmetries are studied in detail. While the particle mass is a Lorentz-invariant quantity, it is shown to be possible to address its variations in terms of the decoherence mechanism in polarization optics.
668406
Quantization of electromagnetic fields in a circular cylindrical cavity
We present a quantization procedure for the electromagnetic field in a circular cylindrical cavity with perfectly conducting walls, which is based on the decomposition of the field. A new decomposition procedure is proposed; all vector mode functions satisfying the boundary conditions are obtained with the help of this decomposition. After expanding the quantized field in terms of the vector mode functions, it is possible to derive the Hamiltonian for this quantized system.
14939249
Coupled Harmonic Oscillators and Feynman's Rest of the Universe
According to Feynman, the universe consists of two parts - the system in which we are interested and the rest of the universe which our measurement process does not reach. Feynman then formulates the density matrix in terms of the observable world and the rest of the universe. It is shown that coupled harmonic oscillators can serve as an illustrative example for Feynman's ``rest of the universe.'' It is pointed out that this simple example has far-reaching consequences in many branches of physics, including statistical mechanics, measurement theory, information theory, thermo-field dynamics, quantum optics, and relativistic quantum mechanics. It is shown that our ignorance of the rest of the universe increases the uncertainty and entropy in the system in which we are interested.
73571003
Time separation as a hidden variable to the Copenhagen school of quantum mechanics
The Bohr radius is a space‐like separation between the proton and electron in the hydrogen atom. According to the Copenhagen school of quantum mechanics, the proton is sitting in the absolute Lorentz frame. If this hydrogen atom is observed from a different Lorentz frame, there is a time‐like separation linearly mixed with the Bohr radius. Indeed, the time‐separation is one of the essential variables in high‐energy hadronic physics where the hadron is a bound state of the quarks, while thoroughly hidden in the present form of quantum mechanics. It will be concluded that this variable is hidden in Feynman’s rest of the universe. It is noted first that Feynman’s Lorentz‐invariant differential equation for the bound‐state quarks has a set of solutions which describe all essential features of hadronic physics. These solutions explicitly depend on the time separation between the quarks. This set also forms the mathematical basis for two‐mode squeezed states in quantum optics, where both photons are observable,...
1320799
Wigner rotations and Iwasawa decompositions in polarization optics.
Wigner rotations and Iwasawa decompositions are manifestations of the internal space-time symmetries of massive and massless particles, respectively. It is shown to be possible to produce combinations of optical filters which exhibit transformations corresponding to Wigner rotations and Iwasawa decompositions. This is possible because the combined effects of rotation, phase-shift, and attenuation filters lead to transformation matrices of the six-parameter Lorentz group applicable to Jones vectors and Stokes parameters for polarized light waves. The symmetry transformations in special relativity lead to a set of experiments which can be performed in optics laboratories.
122939851
Nonstatistical behavior of photoeffect subshell branching ratios at high energies
8523168
Fixed-Point Analysis of the Low-Energy Constants in the Pion-Nucleon Chiral Lagrangian
In the framework of heavy-baryon chiral perturbation theory, we investigate the fixed point structure of renormalization group equations (RGE) for the ratios of the renormalized low energy constants (LECs) that feature in the pion-nucleon chiral Lagrangian. The ratios of the LECs deduced from our RGE analysis are found to be in semi-quantitative agreement with those obtained from direct fit to the experimental data. The naturalness of this agreement is discussed using a simple dimensional analysis combined with Wilsonian RGEs.
28478276
Vector manifestation and fate of vector mesons in dense matter
We describe in-medium properties of hadrons in dense matter near chiral restoration using a Wilsonian matching to QCD of an effective field theory with hidden local symmetry at the chiral cutoff $\Lambda$. We find that chiral symmetry is restored in vector manifestation \`a la Harada and Yamawaki at a critical matter density $n_c$. We express the critical density in terms of QCD correlators in dense matter at the matching scale. In a manner completely analogous to what happens at the critical $N_f^c$ and at the critical temperature $T^c$, the vector meson mass is found to vanish (in the chiral limit) at chiral restoration. This result provides a support for Brown-Rho scaling predicted a decade ago.
18064237
The effect of kaon condensation on quark-antiquark condensate in dense matter
Abstract Assuming that at sufficiently high densities the constituent quarks become relevant degrees of freedom, we study within the framework of a chiral quark model the influence of s -wave K − condensation on the quark–antiquark condensates. We find that, in linear density approximation, the presence of a K − condensate quenches the u ¯ u condensate, but that the d ¯ d condensate remains unaffected up to the chiral order under consideration. We discuss the implication of the suppressed u ¯ u condensate for flavor-dependent chiral symmetry restoration in dense matter.
119341368
A Schematic model for rho - a(1) mixing at finite density and in-medium effective Lagrangian
Based on schematic two-level models extended to a{sub 1}-meson degrees of freedom, we investigate possible mechanisms of chiral restoration in the vector-axial-vector channels in cold nuclear matter. In the first part of this article we employ the massive Yang-Mills framework to construct an effective chiral Lagrangian based on low-energy mesonic modes at finite density. The latter are identified through nuclear collective excitations of ''meson''-sobar type such as {pi}{r_reversible}[{delta}(1232)N{sup -1}]{identical_to}{pi}, {rho}{r_reversible}[N{sup *}(1520)N{sup -1}]{identical_to}{rho}, etc. In a mean-field type treatment the in-medium gauge coupling g, the (axial-)vector meson masses and f{sub {pi}} are found to decrease with density indicating the approach towards chiral restoration in the language of in-medium effective fields. In the second part of our analysis we evaluate the (first) in-medium Weinberg sum rule which relates vector and axial-vector correlators to the pion decay constant. Using in-medium {rho}/a{sub 1} spectral functions (computed in the two-level model) also leads to a substantial reduction of the pion decay constant with increasing density. (c) 2000 The American Physical Society.