Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods

The conservation-law form of the inviscid gasdynamic equations has the remarkable property that the nonlinear flux vectors are homogeneous functions of degree one. This property readily permits the splitting of flux vectors into subvectors by similarity transformations so that each subvector has associated with it a specified eigenvalue spectrum. As a consequence of flux vector splitting, new explicit and implicit dissipative finite-difference schemes are developed for first-order hyperbolic systems of equations. Appropriate one-sided spatial differences for each split flux vector are used throughout the computational field even if the flow is locally subsonic. The results of some preliminary numerical computations are included.     

Lorentz transformations for electromagnetic field vectors and the motion of charges in constant,homogeneous electromagnetic fields

A surface in velocity space which corresponds to Lorentz transformations minimizing the magnitudes of the vectors of a given electromagnetic field is formed. The relation with Lorentz transformations which do not change the magnitudes of the given electromagnetic field is indicated. The behavior of field vectors in a system of reference bound with a charge moving in a constant and homogeneous electromagnetic field is considered. It is shown that an electric charge in a constant and homogeneous electromagnetic field with inclusion of the effect of radiation reaction moves in such a manner that in the reference frame moving with it the magnitudes of the electromagnetic field vectors decrease and their directions approach one another. The time of transition to the state in which the field vectors in the system bound with the charge are mutually parallel is determined.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 11, pp. 63–67, November, 1971.     

Time asymmetric quantum theory – II. Relativistic resonances from S‐matrix poles

Relativistic resonances and decaying states are described by representations of Poincaré transformations, similar to Wigner's definition of stable particles. To associate decaying state vectors to resonance poles of the S‐matrix, the conventional Hilbert space assumption (or asymptotic completeness) is replaced by a new hypothesis that associates different dense Hardy subspaces to the in‐ and out‐scattering states. Then one can separate the scattering amplitude into a background amplitude and one or several “relativistic Breit‐Wigner” amplitudes, which represent the resonances per se. These Breit‐Wigner amplitudes have a precisely defined lineshape and are associated to exponentially decaying Gamow vectors which furnish the irreducible representation spaces of causal Poincaré transformations into the forward light cone.     

On the Symmetry Structures of the Minkowski Metric and a Weyl Re-Scaled Metric

Symmetries of spacetime manifolds which are given by Killing vectors are compared with the symmetries of a Lagrangian constructed from a Weyl re-scaled metric used in discussing disorder operators in Gauge theories. We find the point generators of the one parameter Lie groups of transformations that leave invariant the action integral corresponding to the Lagrangian (Noether symmetries). It is shown that the Noether symmetries obtained by considering the Lagrangian provide additional symmetries which are not provided by the Killing vectors. New conservation law/s are determined.     

Lorentz-boosted evanescent waves

Polarization, spin, and helicity are important properties of electromagnetic waves. It is commonly believed that helicity is invariant under the Lorentz transformations. This is indeed so for plane waves and their localized superpositions. However, this is not the case for evanescent waves, which are well-defined only in a half-space, and are characterized by complex wave vectors. Here we describe transformations of evanescent electromagnetic waves and their polarization/spin/helicity properties under the Lorentz boosts along the three spatial directions.     

Broken symmetry of lie groups of transformation generating general relativistic theories of gravitation

Intransitive Lie groups of transformations have invariant varieties which in suitable cases can be considered as space-times of a universe. The physical laws in the latter are expressed in terms of group theoretical notions. Theorems on the coincidences of group trajectories and geodesics are derived. The groups of linear transformations of the space of basis vectors are used as gauge groups to break the symmetry of the group of transformations and of their natural metric. It is shown that in case of the de Sitter group and its adjoint group as gauge group, one obtains in this way general relativistic theories of gravitation, especially Einstein's theory. More general aspects of the formalism are discussed.Article written in memoriam of B. Jouvet of the Collège de France     

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.     

MOTION OF NEUTRONS IN SLAB-LIKE UNIFORM MAGNETIC FIELDS

The rigorous solutions of the relativistic wave equation for neutrons are obtained in the case of slab-like uniform magnetic fields at perpendicular incidence. For all energy rerions (from zero to ultra-relativistic), corresponding expressions of the one-dimensional scattering of neutrons,in particular, neutrons with very slow velocities, are studied. Finally, the corresponding transformations of the neutron's spin vectors are given.     

Noether Symmetries Versus Killing Vectors and Isometries of Spacetimes

Symmetries of spacetime manifolds which are given by Killing vectors are compared with the symmetries of the Lagrangians of the respective spacetimes. We find the point generators of the one parameter Lie groups of transformations that leave invariant the action integral corresponding to the Lagrangian (Noether symmetries). In the examples considered, it is shown that the Noether symmetries obtained by considering the Larangians provide additional symmetries which are not provided by the Killing vectors. It is conjectured that these symmetries would always provide a larger Lie algebra of which the KV symmetres will form a subalgebra. PACS: 04.25.-g, 02.20.Sv, 11.30.-j     

Kovariante Quantisierung skalarer Felder im Gravitationsfeld

Covariant Quantization of Scalar Fields in a Given Gravitational Field In coupling gravity with the quantum field theory, unitary transformations, depending on space-time-points, are considered and derivatives are introduced, which imply a nonintegrable transport for the state vectors of Hilbert space. The Klein-Gordon-equation, built for scalar field operators with these generalized covariant derivatives, can be quantized now in the same manner in a given gravitational field as the Klein-Gordon-equation in Minkowski space. The quantum state vectors become path dependend. The equations are picture covariant, that is they have the same form in each picture, especially in the Heisenberg picture and the Schrödinger picture.     

The Proof That the Standard Transformations of E and B Are Not the Lorentz Transformations

In this paper it is exactly proved that the standard transformations of the three-dimensional (3D) vectors of the electric and magnetic fields E and B are not relativistically correct transformations. Thence the 3D vectors E and B are not well-defined quantities in the 4D space-time and, contrary to the general belief, the usual Maxwell equations with the 3D E and B are not in agreement with the special relativity. The 4-vectors E ^a and B ^a , as well-defined 4D quantities, are introduced instead of ill-defined 3D E and B. The proof is given in the tensor and the Clifford algebra formalisms.     

Some remarks on local operators in quantum electrodynamics

We assume the existence of a conserved current which generates locally gauge transformations of first kind. We are working in a local quantum Field Theory, where the fields are defined on a vector space where indefinite metric is allowed. We show that the Maxwell equations are not consistent with the above assumptions and the vectors obtained by applying local charged operators on the vacuum cannot describe physical states. Moreover we show that, if charged fields have non-trivial expectation value on the physical states, the vector space must contain vectors with negative norm. We discuss the relation between the local formulation of QED and a formulation in terms of physical states. As an example we study the transition from Gupta-Bleuler free QED to the Coulomb-gauge formulation.     

Quaternionic Lorentz Group and Dirac Equation

We formulate Lorentz group representations in which ordinary complex numbers are replaced by linear functions of real quaternions and introduce dotted and undotted quaternionic one-dimensional spinors. To extend to parity the space-time transformations, we combine these one-dimensional spinors into bi-dimensional column vectors. From the transformation properties of the two-component spinors, we derive a quaternionic chiral representation for the space-time algebra. Finally, we obtain a quaternionic bi-dimensional version of the Dirac equation.     

Lorentz Generators for the Maxwell Field and Gauge Fixing

We propose a direct derivation of the Lorentz generators for the four-potential of electrodynamics on the basis of Wigner's theorem. The derivation relies on a study of the behaviour of polarisation vectors under k-space differentiation. The Coulomb and Lorenz gauges are discussed in that respect, and gauge invariance under Poincare′transformations is examined. The Poincar′e generators given by Bia lynicki-Birula and Bia lynicka-Birula are found to correspond to the Coulomb gauge case.     

Gauge invariance and gauge independence of the S-matrix in nonrelativistic quantum mechanics and relativistic quantum field theories

The gauge independence of transition rates as opposed to the gauge invariance of the equations of motion and gauge dependence of operators and state vectors is critically examined and explicitly demonstrated, both in nonrelativistic quantum mechanics and quantum field theory. Time independent as well as time dependent gauge transformations are explicitly analyzed using several techniques in order to clarify the physical content and significance of gauge independence and the conditions for its applicability.     

Families of singular and subsingular vectors of the topological N = 2 superconformal algebra

We analyze several issues concerning the singular vectors of the topological N = 2 superconformal algebra. First we investigate which types of singular vectors exist, regarding the relative U(1) charge and the BRST-invariance properties, finding four different types in chiral Verma modules and twenty-nine different types in complete Verma modules. Then we study the family structure of the singular vectors, every member of a family being mapped to any other member by a chain of simple transformations involving the spectral flows. The families of singular vectors in chiral Verma modules follow a unique pattern (four vectors) and contain subsingular vectors. We write down these families until level 3, identifying the subsingular vectors. The families of singular vectors in complete Verma modules follow infinitely many different patterns, grouped roughly in five main kinds. We present a particularly interesting thirty-eight-member family at levels 3, 4, 5, and 6, as well as the complete set of singular vectors at level 1 (twenty-eight different types). Finally we analyze the Dörrzapf conditions leading to two linearly independent singular vectors of the same type, at the same level in the same Verma module, and we write down four examples of those pairs of singular vectors, which belong to the same thirty-eight-member family.     

Critical comments on the discussion about tachyonic causal paradoxes and on the concept of superluminal reference frame

The discussions of the tachyonic causal paradoxes and the concept of superluminal reference frame are criticized. The essence of the construction of the known paradoxes is revealed. Some possibilities of eliminating these paradoxes without contradicting the theory of relativity, are discussed. The tachyonic causal loop in an arbitrarily dimensional flat space-time is formally defined. The logical relations between assumptions on existence (or nonexistence) of the tachyonic causal loops and of inertial reference frames preferred in the tachyon kinematics are given. Such frames are not preferred in relation to bradyons and luxons, and maybe are not preferred in the dynamics of the tachyons. The theorem is proved which shows that the discussion on the tachyonic causal loops concerns also the preferred frames. The operational definitions of spacelike, timelike, and null vectors are given. It is shown that superluminal transformations and reference frames do not exist inside the theory of relativity. It is also shown that the so-called superluminal Lorentz transformations are not in fact transformations but mappings. It is concluded that the existence of tachyonic phenomena is not contradictory to the theory of relativity, while the concept of usual superluminal reference frame is contradictory to that theory.     

尺度不变特征与几何特征融合的人耳识别方法

要提高人耳的识别率,关键是特征的提取与表达.尺度不变特征变换(SIFT)技术是局部点特征提取算法,在尺度空间寻找极值点,提取对图像的尺度和旋转变化具有不变性,对光照变化和图像变形具有较强的适应性的特征向量.尝试用SIFT技术来提取外耳图像的结构特征点以形成稳定的特征描述子,为了克服一幅图像中有多个局部描述子相似的问题,在SIFT特征描述子中融入一个耳廓几何特征.最后采用特征向量的欧氏距离作为两幅图像相似性度量标准进行人耳识别.在耳图像库七进行实验.结果表明,该方法不仅可以有效地提取人耳特征,通过少量特征可获得较高的识别率,而且对耳图像刚体变化具有较强的稳健性.     

Doppler effect in a rotating frame

Transformations of complex wave vectors decribing both plane and helical waves are examined on the basis of new complex relativistic transformations including orbital and rotational motions along with the usual. A consequence of these transformations is a generalized Doppler effect, which takes into account possible rotations of the light source. As a result of the motion and rotation of the light source, its emission spectrum will be shifted either to the red or to the blue, depending on the magnitudes of the translational and rotational velocities and the angle between their directions. An experiment is suggested to verify the effect of rotation of the light source on its emission spectrum.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 19–22, July, 1990.