119506678
Lorentz Covariance and Internal Space-time Symmetry of Relativistic Extended Particles
The difference between Lorentz invariance and Lorentz covariance is discussed in detail. A covariant formalism is developed for the internal space-time symmetry of extended particles, especially in connection with the insightful observations Feynman made during the period 1969-72. A Lorentz-group formalism is presented for the harmonic oscillator model of Feynman, Kislinger and Ravndal, which was originally based on hadronic mass spectra. This covariant version allows us to construct a parton distribution function by Lorentz-boosting the oscillator wave function of a hadron at rest. The role of the time-separation variable is discussed in detail. It is shown that, due to our inability to make measurements on this variable, it belongs to Feynman's rest of the universe. Our failure to observe the rest of the universe leads to an increase in entropy.
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,...
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.
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.
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.
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.
14332037
Mass and Spin Measurement with M(T2) and MAOS Momentum
We discuss the M T 2 -kink method to determine the masses of both the dark matter WIMP and its mother particle produced at the LHC. We then introduce a new kinematic variable, the M T 2 -Assisted-On-Shell (MAOS) momentum, that provides a systematic approximation to the invisible particle momenta in hadron collider events producing a pair of invisible particles, and apply it to certain SUSY processes and their UED equivalents to determine the spin of gluino/KK-gluon and of slepton/KK-lepton. An application of the MAOS momentum to the SM Higgs mass measurement is briefly discussed also.
1457184
The Vector and Axial-Vector Susceptibilities and Effective Degrees of Freedom in the Vector Manifestation
The question as to what the relevant degrees of freedom are at the thermal chiral phase transition is addressed in terms of the “vector manifestation (VM)” of chiral symmetry à la Harada and Yamawaki. We find that both the vector susceptibility χV and the axial-vector susceptibility χA at the chiral transition could receive contributions from other degrees of freedom than pions in the chiral limit. The possible candidates are zero-mass vector mesons and quasiquarks. In the presence of these degrees of freedom, hidden local symmetry (HLS) theory with vector manifestation predicts that χV equals χA in consistency with chiral invariance and that both the time component f t π and the space component f s π of the pion decay constant vanish at the chiral phase transition. With the VM, the pion velocity vπ proportional to f s π/f t π at T = Tc is predicted to be equal to 1. These results are obtained in the leading order in power counting but we expect them to hold more generally in the chiral limit thanks to the VM point. and Department of Physics and Astronomy, University of South Carolina, Columbia, SC 29208 and School of Physics, Korea Institute for Advanced Study, Seoul 130-012, Korea.
119289779
M(T2)-assisted on-shell reconstruction of missing momenta and its application to spin measurement at the LHC
We propose a scheme to assign a 4-momentum to each WIMP in new physics event producing a pair of mother particles each of which decays to an invisible weakly interacting massive particle (WIMP) plus some visible particle(s). The transverse components are given by the value that determines the event variable M{sub T2}, while the longitudinal component is determined by the on-shell condition on the mother particle. Although it does not give the true WIMP momentum in general, this M{sub T2}-assisted on-shell reconstruction of missing momenta provides kinematic variables well correlated to the true WIMP momentum and thus can be useful for an experimental determination of new particle properties. We apply this scheme to some processes to measure the mother particle spin and find that spin determination is possible even without good knowledge of the new particle masses.
5119942
Measuring superparticle masses at hadron collider using the transverse mass kink
We present a detailed study of the collider observable mT2 applied for pair-produced superparticles decaying to visible particles and a pair of invisible lightest supersymmetric particles (LSPs). Analytic expressions of the maximum of mT2 over all events (mT2max) are derived. It is noticed that if the decay product of each superparticle involves more than one visible particle, mT2max being a function of the trial LSP mass mχ has a kink structure at mχ = true LSP mass, which can be used to determine the mother superparticle mass and the LSP mass simultaneously. To see how well mT2max can be constructed from collider data, a Monte-Carlo analysis of the gluino mT2 is performed for some superparticle spectra.
2251108
Competition Between Induced Symmetry Breaking, Cooper Pairing and Chiral Condensate at Finite Density
We study the competition between induced symmetry breaking (ISB), 
Cooper pairing (superconductivity) and chiral condensation at finite non-asymptotic density. Using a quantum mechanical model studied recently by Ilieva and Thirring, we analyze the expectation value of the fermion number density $\la a^*a\ra$ in the presence of chemical potential and discuss relevance of the ISB phenomenon in the model. By Bogoliubov transformation, we obtain the ground state energy and find that a phase with both superconducting and mean field gap is a true ground state. We also study the effective potentials of a two-dimensional field theory model for competitions between $\la\bar\psi\psi\ra$, $\la\psi\psi\ra$ and $\la\psi^\dagger\psi\ra$. We find that in the regime $\mu \mu_c$ the system sits in the mixed phase characterized by 
$\la \psi^\dagger\psi\ra\neq 0$ and $\la \psi\psi\ra\neq 0$ as long as the renormalization point, $M_0$, corresponding to a superconducting gap is not zero, $M_0\neq 0$.