Fermions and bosons in a two-dimensional world

We derive the formal equivalence of a free massless two-dimensional theory and a free massless two-dimensional boson theory constructed from the bilinear products of the self-same fermion theory. The sense of this equivalence is investigated. Using a box normalization, it is found that the fermion states are Glauber coherent states of bosons, where the boson vacuum is the ground state of the charge sector corresponding to the given fermion state. The massless boson is the Goldstone boson and the degenerate vacua are the ground states of the various charge sectors. A complete operator identity between fermion and boson operators can be obtained, but to do this an additional boson operator must be introduced which cannot be defined in terms of bilinear products of the fermion operators. Doing this makes the charge spectrum continuous.     

Interacting fermions on a random lattice

We extend previous work on the properties of the Dirac lagrangian on two-dimensional random lattices to the case where interaction terms are included. Although for free fermions the chiral symmetry of the doubles is spontaneously broken by their interaction with the lattice and they decouple from long-distance physics, our results in this paper show that all is undone by quantum corrections in an interacting field theory and that the end result is very similar to what is found with Wilson fermions. Two field-theoretical models with interacting fermions are studied by perturbation expansion in the field theory coupling constant. These are a model with one fermion and one boson species interacting via a scalar Yukawa coupling and the massive Thirring model. It is shown that on the random lattice ultraviolet finite diagrams and finite parts of ultraviolet divergent diagrams have the correct continuum limit. Ultraviolet divergent parts can be removed by the same renormalisation procedure as in the continuum, but do not exhibit the same dependence on the lagrangian mass. In the case of the massive Thirring model this causes a fermion mass correction of order the cut-off scale, which breaks the chiral symmetry of the remaining light fermion; there is consequently a fine-tuning problem. In the context of the same model we discuss the effect of the Goldstone boson associated with the spontaneous breakdown of the chiral symmetry of the doubles on two-dimensional models with vector couplings.     

Testing Gravity on Astrophysical Scales

We summarize a series of observational tests of the law of gravity on large astrophysical scales. These tests account for testing both the Poisson equation (inverse square law) using weak lensing and the Einstein equivalence principle through the test of the constancy of the constants of Nature. We emphasize the need to test general relativity on cosmological scales in light of the cosmological constant problem and of recent observational claims concerning the variation of fine structure constant.     

Z2-twisted fields and bosonization on Riemann surfaces

The equivalence on Riemann surfaces between one Z₂-twisted boson and two fermions having different spin structures is proved. The equivalence is shown on the partition function and on the N-point functions. We analyse the consistency between the chiral and the non-chiral definitions of the twisted vertex operator. The equivalence essentially relies upon the eighty year old Schottky-Jung identities.     

Helicity conservation in gauge boson scattering at high energy

We remark that the high energy gauge boson scattering processes involving two-body initial and final states satisfy certain selection rules described as helicity conservation of the gauge boson amplitudes (GBHC). These rules are valid at the Born level, as well as at the level of the leading and subleading 1-loop logarithmic corrections, in both the standard model and the minimal supersymmetric standard model (MSSM). A "fermionic equivalence" theorem is also proved, which suggests that GBHC is valid at all orders in the MSSM at sufficiently high energies, where the mass suppressed contributions are neglected.     

Decoherence and infrared divergence

The dynamics of a particle which is linearly coupled to a boson field is investigated. The boson field induces superselection rules for the momentum of the particle, if the field is infrared divergent. Thereby the Hamiltonian of the total system remains bounded from below.     

Instability of a two-dimensional Bose–Einstein condensate with Rashba spin–orbit coupling at finite temperature

We prove that in a two-dimensional homogeneous boson system with Rashba spin–orbit coupling, Bose–Einstein condensate with plane-wave order is unstable at finite temperature. The calculations are based on a nonlinear sigma model scheme. The density wave contributions to the thermal deletions are divergent in the infrared limit. The behavior of the divergence is different from that without spin–orbit coupling.     

Theory of quantum dynamics in fermionic environment: An influence functional approach

Quantum dynamics of a particle coupled to a fermionic environment is considered, with particular emphasis on the formulation of macroscopic quantum phenomena. The framework is based on a path integral formalism for the real-time density matrix. After integrating out of the fermion variables of the environment, we embed the whole environmental effects on the particle into the so-called influence functional in analogy to Feynman and Vernon's initial work. We then show that to the second order of the coupling constant, the exponent of the influence functional is in exact agreement with that due to a linear dissipative environment (boson bath). Having obtained this, we turn to a specific model in which the influence functional can be exactly evaluated in a long-time limit (long compared to the inverse of the cutoff frequency of the environmental spectrum). In this circumstance, we mainly address our attention to the quantum mechanical representation of the system-plus-environment from the known classical properties of the particle. It is shown that, in particular, the equivalence between the fermion bath and the boson bath is generally correct for a singlechannel coupling provided we make a simple mapping between the nonlinear interaction functions of the baths. Finally, generalizations of the model to more complicated situations are discussed and significant applications and connections to certain practically interesting problems are mentioned.     

Boson–boson pure-dephasing model with non-Markovian properties

In this paper, we discuss the mechanism of pure-dephasing process with a newly proposed boson–boson model, namely, a bosonic field coupled to another bosonic bath in thermal equilibrium. Our model is fully solvable and can reproduce the pure-dephasing process which is usually described by the well-known spin–boson model, therefore offering a new perspective to understanding decoherence processes in open quantum systems of high dimension. We also show that this model admits a generically non-Markovian dynamics with respect to various different non-Markovian characterizations, i.e., the criteria based on divisibility, quantum regression formula and Wigner function, respectively. The criterion based on Wigner function is firstly proposed in this paper. For the case that the particle number of the pure-dephasing system is constrained to be 0 or 1, we analytically prove its equivalence to the criteria based on trace distance and divisibility.     

THE CORRESPONDENCE PRINCIPLE IN (1+1)-DIMENSIONAL FIELD THEORY AND THE COLEMAN THEOREM

The correspondence relations between a fermion field and a boson field in (1+1)-dimensional quantum field theory is discussed in general. Emphases have been laid on the renorinalization with respect.to an arbitrary mass parameter in boson version as well as the nonlocal property of currents in fermion version. After establishing the equivalence between the continuous chiral transformation in fermion version and the translational transformation in boson version, we are able to prove the Coleman theorem correspondingly.     

A Canonical Ensemble Approach to the Fermion/Boson Random Point Processes and Its Applications

We introduce the boson and the fermion point processes from the elementary quantum mechanical point of view. That is, we consider quantum statistical mechanics of the canonical ensemble for a fixed number of particles which obey Bose-Einstein, Fermi-Dirac statistics, respectively, in a finite volume. Focusing on the distribution of positions of the particles, we have point processes of the fixed number of points in a bounded domain. By taking the thermodynamic limit such that the particle density converges to a finite value, the boson/fermion processes are obtained. This argument is a realization of the equivalence of ensembles, since resulting processes are considered to describe a grand canonical ensemble of points. Random point processes corresponding to para-particles of order two are discussed as an application of the formulation. Statistics of a system of composite particles at zero temperature are also considered as a model of determinantal random point processes.     

Note on Higgs Decay into Two Photons H → γγ

The Higgs decay H →γγ due to the virtual W-loop effect is revisited in the unitary gauge by using the symmetry-preserving and divergent-behavior-preserving loop regularization method,which is realized in the fourdimensional space-time without changing original theory.Though the one-loop amplitude of H →γγ is finite as the Higgs boson in the standard model has no direct interaction with the massless photons at tree level,it involves both tensor-type and scalar-type divergent integrals which can in general destroy the gauge invariance without imposing a proper regularization scheme to make them well-defined.As the loop regularization scheme can ensure the consistency conditions between the regularized tensor-type and scalar-type divergent irreducible loop integrals to preserve gauge invariance,we explicitly show the absence of decoupling in the limit M W /M H → 0 and obtain a result agreeing exactly with the earlier one in the literature.We then clarify the discrepancy of the earlier result from the recent one obtained by R.Gastmans,S.L.Wu and T.T.Wu.The advantage of calculation in the unitary gauge becomes manifest in that the non-decoupling arises from the longitudinal contribution of the W gauge boson.     

Cosmic strings in a space–time with positive cosmological constant

We study Abelian strings in a fixed de Sitter background. We find that the gauge and Higgs fields extend smoothly across the cosmological horizon and that the string solutions have oscillating scalar fields outside the cosmological horizon for all currently accepted values of the cosmological constant. If the gauge to Higgs boson mass ratio is small enough, the gauge field function has a power-like behaviour, while it is oscillating outside the cosmological horizon if Higgs and gauge boson mass are comparable. Moreover, we observe that Abelian strings exist only up to a maximal value of the cosmological constant and that two branches of solutions exist that meet at this maximal value. We also construct radially excited solutions that only exist for non-vanishing values of the cosmological constant and are thus a novel feature as compared to flat space–time. Considering the effect of the de Sitter string on the space–time, we observe that the deficit angle increases with increasing cosmological constant. Lensed objects would thus be separated by a larger angle as compared to asymptotically flat space–time.     

The decay constant of the holographic techni-dilaton and the 125 GeV boson

We critically discuss the possibility that the 125 GeV boson recently discovered at the LHC is the holographic techni-dilaton, a composite state emerging from a strongly-coupled model of electroweak symmetry breaking. This composite state differs from the SM for three main reasons. Its decay constant is in general larger than the electroweak scale, hence suppressing all the couplings to standard-model particles with respect to an elementary Higgs boson, with the exception of the coupling to photons and gluons, which is expected to be larger than the standard-model equivalent.     

Determination of the electroweak chiral-lagrangian parameters at the LHC

In this work we report on the results obtained in a detailed and systematical study of the possibility to measure the parameters appearing in the electroweak chiral lagrangian. The main novelty of our approach is that we do not use the equivalence theorem and therefore we work explicitly with all the gauge boson degrees of freedom.     

Determination of the electroweak chiral-lagrangian parameters at the LHC

In this work we report on the results obtained in a detailed and systematical study of the possibility to measure the parameters appearing in the electroweak chiral lagrangian. The main novelty of our approach is that we do not use the equivalence theorem and therefore we work explicitly with all the gauge boson degrees of freedom.     

Fermions and associated bosons of one-dimensional model

The representation of the canonical commutation relations involved in the construction of boson operators from fermion operators according to the recipe of the neutrino theory of light is studied. Starting from a cyclic Fock-representation for the massless fermions the boson operators are reduced by the spectral projectors of two charge-operators and form an infinite direct sum of cyclic Fock-representations. Kronig's identity expressing the fermion kinetic energy in terms of the boson kinetic energy and the squares of the charge operators is verified as an identity for strictly selfadjoint operators. It provides the key to the solubility ofLuttinger's model. A simple sufficient condition is given for the unitary equivalence of the representations linked by the canonical transformation which diagonalizes the total Hamiltonian.Work supported by the National Science Foundation.     

Two and Three Cocycles in a Hybrid Chiral Bag Model (A Comment on the Bosonization of Fermions)

In this paper, a 3-cocycle is realized in a hybrid chiral bag model as quantities at the boundary of the bag. The equivalence between charges of gauged boson currents in Skyrme model and full gauge transformation generators is established both in 3+1 dimensions and 1+1 dimensions.     

The Principle of Equivalence and the Twin Paradox

No Heading The canonical twin paradox is explained by making a correct use of the principle of equivalence. The role of the principle of equivalence is to provide a physical agent i.e gravity which can supply the required extra aging to the rocket-bound sibling during its acceleration phase through a gravitational time-offset effect. We follow an approach where a novel variation on the twin paradox is used to connect gravity with the desynchronization in the clocks of two spatially distant, identically accelerated observers. It is shown that this approach removes certain drawbacks of an earlier effort which claims to exploit the equivalence principle in explaining the differential aging in the paradox. * Author to whom all correspondences should be made.