International Journal of Modern Physics A

We give a review of some group-theoretical results related to nonrelativistic holography. Our main playgrounds are the Schrödinger equation and the Schrödinger algebra. We first recall the interpretation of nonrelativistic holography as equivalence between representations of the Schrödinger algebra describing bulk fields and boundary fields. One important result is the explicit construction of the boundary-to-bulk operators in the framework of representation theory, and that these operators and the bulk-to-boundary operators are intertwining operators. Further, we recall the fact that there is a hierarchy of equations on the boundary, invariant with respect to Schrödinger algebra. We also review the explicit construction of an analogous hierarchy of invariant equations in the bulk, and that the two hierarchies are equivalent via the bulk-to-boundary intertwining operators. The derivation of these hierarchies uses a mechanism introduced first for semisimple Lie groups and adapted to the nonsemisimple Schrödinger algebra. These require development of the representation theory of the Schrödinger algebra which is reviewed in some detail. We also recall the q-deformation of the Schrödinger algebra. Finally, the realization of the Schrödinger algebra via difference operators is reviewed.

We review the properties of highly excited states in string theory with a focus on the decay process. We first survey the decay of a fundamental string with various setups. We then discuss the decay rate of averaged excited states of superstrings and obtain the emission spectrum which takes a form of thermal radiation. We finally examine the emission spectrum in the context of the black hole/string correspondence à la Susskind.

In this paper, we describe our recent work on discrete quantum theory based on Galois fields. In particular, we discuss how discrete quantum theory sheds new light on the foundations of quantum theory and we review an explicit model of super-quantum correlations we have constructed in this context. We also discuss the larger questions of the origins and foundations of quantum theory, as well as the relevance of super-quantum theory for the quantum theory of gravity.

To understand better the quantum structure of field theory and standard model in particle physics, it is necessary to investigate carefully the divergence structure in quantum field theories (QFTs) and work out a consistent framework to avoid infinities. The divergence has got us into trouble since developing quantum electrodynamics in 1930s. Its treatment via the renormalization scheme is satisfied not by all physicists, like Dirac and Feynman who have made serious criticisms. The renormalization group analysis reveals that QFTs can in general be defined fundamentally with the meaningful energy scale that has some physical significance, which motivates us to develop a new symmetry-preserving and infinity-free regularization scheme called loop regularization (LORE). A simple regularization prescription in LORE is realized based on a manifest postulation that a loop divergence with a power counting dimension larger than or equal to the space–time dimension must vanish. The LORE method is achieved without modifying original theory and leads the divergent Feynman loop integrals well-defined to maintain the divergence structure and meanwhile preserve basic symmetries of original theory. The crucial point in LORE is the presence of two intrinsic energy scales which play the roles of ultraviolet cutoff M_c and infrared cutoff μ_s to avoid infinities. As M_c can be made finite when taking appropriately both the primary regulator mass and number to be infinity to recover the original integrals, the two energy scales M_c and μ_s in LORE become physically meaningful as the characteristic energy scale and sliding energy scale, respectively. The key concept in LORE is the introduction of irreducible loop integrals (ILIs) on which the regularization prescription acts, which leads to a set of gauge invariance consistency conditions between the regularized tensor-type and scalar-type ILIs. An interesting observation in LORE is that the evaluation of ILIs with ultraviolet-divergence-preserving (UVDP) parametrization naturally leads to Bjorken–Drell's analogy between Feynman diagrams and electric circuits, which enables us to treat systematically the divergences of Feynman diagrams and understand better the divergence structure of QFTs. The LORE method has been shown to be applicable to both underlying and effective QFTs. Its consistency and advantages have been demonstrated in a series of applications, which includes the Slavnov–Taylor–Ward–Takahaski identities of gauge theories and supersymmetric theories, quantum chiral anomaly, renormalization of scalar interaction and power-law running of scalar mass, quantum gravitational effects and asymptotic free power-law running of gauge couplings.

The LHCb collaboration has recently reported evidence for nonzero CP asymmetries in B⁺ decays into π⁺K⁺K^-, π⁺π⁺π^-, K⁺K⁺K^- and K⁺π⁺π^-. The branching ratios for these decays have also been measured with different values ranging from 5×10^-6 to 51×10^-6. If flavor SU(3) symmetry is a good symmetry for B decays, in the case that the dominant amplitude is momentum independent it is expected that branching ratios Br and CP violating rate differences satisfy, Br(π⁺π⁺π^-) = 2 Br(π⁺K⁺K^-), Br(K⁺K⁺K^-) = 2 Br(K⁺π⁺π^-) and Δ_CP(π⁺π⁺π^-) = 2Δ_CP(π⁺K⁺K^-) = -Δ_CP(K⁺K⁺K^-) = -2Δ_CP(K⁺π⁺π^-). The experimental data do not exhibit the expected pattern for the branching ratios. The rate differences for B⁺→π⁺π⁺π^- and B⁺→K⁺ K⁺ K^- satisfy the relation between ΔS = 0 and ΔS = 1 as well, but the other two do not, with the CP asymmetries having different signs than expected. In this paper, we study how to include momentum dependent and also SU(3) breaking effects on these decays to explain experimental data. We find that by including only the lowest order derivative terms, in the SU(3) limit, the decay patterns cannot be explained. Large SU(3) breaking effects are needed to explain the data.

We demonstrate the monopole condensation in SU(3) QCD. We first discuss the gauge independent and Weyl symmetric Abelian (Cho-Duan-Ge) decomposition of the SU(3) QCD, and present a new gauge invariant integral expression of the one-loop effective action which has no infrared divergence. Integrating it gauge invariantly imposing the color reflection invariance ("the C-projection") we show that the effective potential generates the stable monopole condensation which generates the mass gap.

Processes τ→lγ, τ→lll with l = e, μ and μ(τ) →e (μ) γ are evaluated in the framework of a model based on the extended symmetry gauge SU(3)_c ⊗SU(3)_L ⊗U(1)_Y with a leptonic sector consisting of five triplets. Lepton flavor violating processes are allowed at tree level in this model through the new Z′ gauge boson. We obtained bounds for the mixing angles in the leptonic sector of the model, considering the experimental measurements of the processes from the BELLE and the BABAR collaborations.

We analyzed the identified hadron multiplicity predictions of the generalized thermodynamical model of the multiparticle production processes with nonextensive statistics. The multiplicities measured recently at LHC experiments seem to be consistent with this approach and thermodynamical parameter values are found already by analyzing transverse momentum distributions. The information about the mechanism of the strangeness suppression has been derived to some extent from multistrange hadron abundances.

We develop the general relativity of extended spacetime–property for describing events including their properties. The anticommuting nature of property coordinates, augmenting spacetime (x, t), allows for the natural emergence of generations and for the simple incorporation of gauge fields in the spacetime–property sector. With one electric property, this results in a geometrical unification of gravity and electromagnetism, leading to a Maxwell–Einstein Lagrangian plus a cosmological term. Addition of one neutrinic and three chromic properties should lead to unification of gravity with electroweak and strong interactions.

Following the procedures by which O(N)-invariant real vector models and their large-N behavior have previously been solved, we extend similar techniques to the study of real symmetric N×N-matrix models with O(N)-invariant interactions. Proper extensions to N = ∞ are also established. While no 1/N-expansions are involved in our analysis, a brief comparison of our procedures with traditional 1/N-expansion procedures is given.

We present a general analysis of gauge invariant, exact and metric independent forms which can be constructed using higher-rank field-strength tensors. The integrals of these forms over the corresponding space–time coordinates provides new topological Lagrangians. With these Lagrangians one can define gauge field theories which generalize the Chern–Simons quantum field theory. We also present explicit expressions for the potential gauge anomalies associated with the tensor gauge fields and classify all possible anomalies that can appear in lower dimensions.