Dynamical systems with the Bäcklund transformation

We propose a method which enables to find field theories in 1 + 1 dimensions with the Bäcklund transformation.Dedicated to Academician Václav Votruba on the occasion of his seventieth birthday.     

The use of projective limits in classical statistical mechanics and Euclidean quantum field theory

The Gibbs states of an infinite classical statistical system correspond to the states of reservoir at infinity. It is shown that its configuration space can be thought of as a generalized projective limit of configuration spaces of remote reservoirs. This notion of projective limit is defined and it is noted that it can also be used e.g. for proofs of the existence of Gibbs states in the thermodynamic limit and their decomposition into pure phase. A similar approach to (nonperturbative) Euclidean quantum field theory is suggested and connections with the concept of renormalizability are found.Dedicated to Academician Václav Votruba on the occasion of his seventieth birthday.The first-named author (R. K.) would like to express his thanks to Prof. V. Votruba for general support and constant encouragement.     

Wave functions of unstable particles

The assumptions necessary for the determination of the wave functions of unstable particles are formulated.Dedicated to Professor V. Votruba on his sixtieth birthday.On leave of absence from Charles University, Prague, Czechoslovakia.The author is indebted to Prof. V. Votruba for his support and stimulating discussions. He would further like to thank Prof. H. Leutwyler and Prof. A. Mercier for hospitality in Berne and for various suggestions.     

Glueball mass estimate by strong coupling expansion in lattice gauge theories

In the formalism presented in the previous paper, the plaquette-plaquette correlation functions in arbitrary directions are calculated for Z(2), SU(2) and SU(3) up to order g^?8. Approximate restoration of rotational symmetry is observed in the continuum limit for SU(2), but much higher order corrections seem to be required in order to restore the symmetry for SU(3). The scalar glueball mass deduced from the plaquette-plaquette correlation function in the diagonal direction is 0.80 GeV, while the on-axis computation up to order g^?16 predicts it to be 0.64 GeV.     

An analysis of the principle of minimal electromagnetic interaction

The meaning and contents of the principle of minimal electromagnetic interactions are analyzed in the framework of the classical electrodynamics of a point charged particle. The essence of this analysis consists in expressing the free electromagnetic field as a difference of retarded and advanced fields and in observing the effect of switching on the minimal coupling on the retarded field. A new equivalent formulation of this principle is given and the possibility of its generalization is suggested.Dedicated to Professor V. Votruba on his sixtieth birthday.     

Chiral symmetry restoration in baryon rich environments

Chiral symmetry restoration in an environment rich in baryons is studied by computer simulation methods in SU(2) and SU(3) gauge theories in the quenched approximation. The basic theory of symmetry restoration as a function of chemical potential is illusstrated and the implementation of the ideas on a lattice is made explicit. A simple mean field model is presented to guide one's expectations. The second order conjugate-gradient iterative method and the pseudo-fermion Monte Carlo procedure are convergent methods of calculating the fermion propagator in an environment rich in baryons. Computer simulations of SU(3) gauge theory show an abrupt chiral symmetry restoring transition and the critical chemical potential and induced baryon density are estimated crudely. A smoother transition is observed for the color group SU(2).     

The SU(8) GUT for chiral families

We argue that there is a natural inclusion of the standard model with the family-unified chiral local symmetry SU(3)_H in a new SU(8) GUT inspired by Georgi's SU(11) model. The SU(8) symmetry breaking along the chain with the intermediate electro-weak-horizontal unification SU(8)→SU(5)_EWH×SU(3)_c×U(1) is proved d to be the distinguished pattern. The model predicts a long-lived proton (10³³–10³⁵yr) and practically the observed value of the Weinberg angle, in sharp contrast to the ordinary GUTs. The observation of the specific flavour-changing baryon decays (p→π,μ,Ke,…) could unambiguously single out the flavour unified GUTs as well as confirm the existence of the elementary horizontal forces at small distances.     

Non-Grassmannian approach to spinning particles

A classical model of spinning particle is elaborated for the purpose of path integrals. The model is defined in terms of conventional commuting variables, as opposed to models based on Grassmannian variables.Dedicated to Academician Václav Votruba on the occasion of his eightieth birthday.     

Magnetic moments of baryons in higher symmetry schemes including charm

Relations among the magnetic moments of charmed and uncharmed baryons are derived in the framework of SU(4) and SU(8) symmetries. The SU(3) resultμ (Σ ^o)=−μ(Λ) is not present in SU(4), but is obtained in SU(8). Higher order effects are further considered to improve the situation.     

Properties of SO(8) extended supergravity

The conjectured SU(8) invariance of the field equations of SO(8) extended supergravity is used to elucidate the general structure of the extended theories. Due to the representation content of the spinless fields this does not lead to a complete determination of the theory, as was the case for N = 4. The non-polynomial modifications by spinless fields are given in terms of a number of SU(8) covariant tensors, for which various identities are derived and discussed.     

PARISI-SOURLAS CONFINEMENT MECHANISM OF QUANTUM CHROMODYNAMICS

Using Parisi and Sourlas dimensional reduction, four-dimensional quantum chromodynamics is reduced to a two-dimensional principal chiral model by suitable superspace embedding. The frame T^a cannot be regarded as a fixed one and the frame connection field \varω_μ(x) becomes a dynamical gauge field in two dimensions, giving rise to a confining potential. As a result of the original SU(3) Yang-Mills field obtains another SU(3) local symmetry and turns into SU(3)×SU(3) local symmetry－one group element as exp (iδ\varphi^aT^a) with fixed frame T^a, the other gauging the frame T^a.     

Some features of SU(4) symmetry

Representations and generators for SU(4) symmetry are obtained SU(3) content of SU(4) is derived. A general formula for the c.c. series of the direct product of two representations of SU(4) symmetry is obtained.The author is thankful to Mr. R. S.Sharma for his kind assistance and encouragements, due to which he was able to complete this work for publication.     

Reduction of capillary force for high-aspect ratio nanofabrication

The wet processing of SU8 resist was modified in order to achieve a high-aspect ratio patterning with feature size of 100 nm. A final rinse in water, which makes a large contact angle on the resist (less wetting) was added to the procedure. This allowed considerable reduction of the capillary force, which is responsible for pattern distortions in three-dimensional (3D) lithography. 3D recording of high-aspect ratio (f_ar=18) structures by holographic exposure using femtosecond pulses in SU8 resist was achieved using this modified development procedure. The thickness of the free-standing planes was approximately 100 nm. High fidelity of this recording method was confirmed by a Moiré pattern transfer into a developed SU8 pattern. In terms of focusing, the 100 nm feature size comprised 1/13-th of the diffraction limit. This modified development is applicable for wet processing when super-critical drying cannot be used. PACS 81.05.-t; 81.07.-b; 81.16.-c; 81.40.-z; 81.65.-b     

A hidden Higgs lagrangian in QCD

It is shown that a previously found instability for the SU(2) Yang-Mills field equation can be removed by a (1 + 1) dimensional Higgs mechanism. The SU(2) results are generalized to SU(N), with special emphasis on SU(3).     

Improved QCD vacuum for gauge groups SU(3) and SU(4)

The effective energy for a covariantly constant background field in a pure Yang-Mills theory is calculated to loop order one. For gauge group SU(3) [SU(4)] it is found that the “vacuum” configuration consists of two [three] constant color magnetic fields of equal non-zero magnitude orthogonal to each other in color as well as physical space. We conclude that the structure of the Copenhagen vacuum is more complex than previously expected.     

Ferroquadrupolar Order in the Spin-1 Bilinear-Biquadratic Model up to the Second Nearest Neighbor

We have studied some ferroquadrupolar phases of the S = 1 Heisenberg model with bilinear and biquadratic exchange interactions on the square lattice up to the second nearest neighbor, using the SU(3) Schwinger bosons formalism in a mean field approximation. This technique is very convenient to treat nematic order. This technique has the advantage of using the fundamental representation of the SU(N) group instead of SU(2), designed to capture spin-quadrupolar order in addition to the dipolar magnetic order. We also present quadrupole structure factors that can be measured in future experiments. Our calculations can have implications in the study of iron-based superconductors.     

Gauged N = 8 supergravity in five dimensions

We construct gauged N = 8 supergravity theories in five dimensions. Instead of the twenty-seven vector fields of the ungauged theory, the gauged theories contain fifteen vector fields and twelve second-rank antisymmetric tensor fields satisfying self-dual field equations. The fifteen vector fields can be used to gauge any of the fifteen-dimensional semisimple subgroups of SL(6,R), specially SO(p, 6?p) for p = 0, 1, 2, 3. The gauged theories also have a physical global SU(1,1) symmetry which survives from the E₆₍₆₎ symmetry of the ungauged theory. This SU(1,1) for the SO(6) gauging is presumably related to that of the chiral N = 2 theory in ten dimensions. In our formalism we maintain a composite local USp(8) symmetry analogous to SU(8) in four dimensions.     

The mass-scale of supersymmetry breaking and proton decay

A fundamental mass-scale is associated with the transition of supersymmetric SU(3)_c×SU(2)_L×U(1) to the ordinary SU(3)_c×SU(2)_L×U(1) symmetry of elementary particle interactions. The renormalisation of the gauge coupling in a supersymmetric SU(5) grand unification leads to the mass-scale of supersymmetry breaking to be of order 10¹² GeV if the lifetime of the proton is taken to be 10³⁰ y and is lowered to the mass-scale of ordinary electroweak interactions if the proton lives longer than 10³⁰ y. It is lower than 10¹² GeV if the contribution of light scalars is taken into account. The predictions of the weak angle sin²θ (M_W) are in excellent agreement with experiment.     

QCD Dirac spectrum and components of the gauge field

We analyze the relation between the Dirac spectrum and the gauge field in SU(3) lattice QCD. We focus on how a certain component of the gauge field is related to the Dirac spectrum. First, we consider momentum components of the gauge field. It turns out that the broad momentum region is relevant for the low-lying Dirac spectrum and topological charges. The connection with chiral random matrix theory is also discussed. Second, we consider an SU(2) subgroup component of the SU(3) gauge field. The SU(2) subgroup component behaves like the SU(2) gauge field in the low-lying Dirac spectrum.     

A remark on divergence cancellations in the Weinberg-Salam model

An alternative proof of ultraviolet divergence cancellation (at the one-loop level) in certain ratios of renormalized coupling constants in the Weinberg-Salam model is suggested. Working in the unitary gauge, we use a simple coordinate-space method for manipulating Feynman integrals proposed by Kummer and Lane. In a particular example it is shown that this method provides an extremely useful tool for solving the problem.Dedicated to Academician Václav Votruba on the occasion of his seventieth birthday.