On the Equivalence of Regularization Schemes

We illustrate via the sunset diagram that dimensional regularization “deforms“ the nonlocal contents of multi-loop disgrams with its equivalence to cutoff regularization scheme recovered only after sub-divergence was subtracted.Then we employed a differential equation approach for calculationg loop diagrams to verify that dimensional regularization deforms the low energy contents before subtraction.The virtues of the differential equation approach are argued especially in nonperturbative perspective.     

On the “Equivalence” of the Maxwell and Dirac Equations

It is shown that Maxwell's equation cannot be put into a spinor form that is equivalent to Dirac's equation. First of all, the spinor in the representation of the electromagnetic field bivector depends on only three independent complex components whereas the Dirac spinor depends on four. Second, Dirac's equation implies a complex structure specific to spin 1/2 particles that has no counterpart in Maxwell's equation. This complex structure makes fermions essentially different from bosons and therefore insures that there is no physically meaningful way to transform Maxwell's and Dirac's equations into each other.     

Excitation Frequency Effect of Differential Capacitance Transducer for Equivalence Principle Test

We discuss effects of the excitation frequency in an ac bridge differential capacitance transducer for the equivalenceprinciple test on the frequency-dependent characteristics of a practical operational amplifier, the thermal noise limitation, and stray-immune. Basic requirements of choosing the excitation frequency of the ac bridge capacitance transducer are given based on the three effects, which are significant for designing a capacitance transducer and choosing proper electric elements.     

Gaussian Beam Effect on Equivalence Principle Test Using Free—Fall Interferometry

We discuss the gaussian beam effect on the test of the equivalence principle using a free-fall interferometer.A two-lens assembly is used to improve the propagating character of the laser beam,and the beam radius is collimated to about 3.0mm.The analysis shows that the gravity acceleration difference induced by the Gaussian beam effect could be less than 10^-15 g for our double free-fall experimental design,but it would be 10^-9g for the absolute measurement of the gravity acceleration with the usual single free-fall method.     

Further Corroboration of Equivalence of Two χ2 Forms

The equivalence of two χ² forms for linear function fit is proved.The two forms of χ² are applied on a simplified R-value measurement to test the equivalence.     

Equivalence between the Osserman condition and the Rakić duality principle in dimension 4

We show that four-dimensional Riemannian manifolds which satisfy the Raki? duality principle are Osserman (i.e. the eigenvalues of the Jacobi operator are constant). Thus, since it was proved in Raki? (1999) [9] that Osserman manifolds satisfy the Raki? duality principle, both conditions are equivalent.     

Dynamical Behaviour of a Modulated Torsion Pendulum in Test of Weak Equivalence Principle

The dynamic behaviour of a modulated torsion pendulum used to test the weak equivalence principle (WEP) is studied in detail. Theoretical analysis shows that the pendulum will be driven by a force with double-frequency of the rotating turntable no matter whether the WEP is valid or not. This double-frequency effect should be considered for improving the sensitivity of the modulated pendulum in test of the WEP.     

Equivalence principle,the general theory of relativity,ang “black holes”

The equivalence principle is necessary for the validity of Newtonian mechanics, since only in this case can one consider an isolated system, neglecting the attraction of distant bodies. The possibility of verifying the equivalence principle by observations of the structure of galaxies and the large-scale structure of the universe is discussed. It is pointed out that the existence of horizons with valve properties -a one-way exchange of information—contradicts the equivalence principle.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 11–15, January, 1984.     

Does the Principle of Equivalence Prohibit Trapped Surfaces from Forming in the General Relativistic Collapse Process?

It has recently been shown that time-like spherical collapse of a physical fluid in General Relativity does not permit formation of trapped surfaces. This result followed from the fact that the formation of a trapped surface in a physical fluid would cause the time-like world lines of the collapsing fluid to become null at the would-be trapped surface, thus violating the Principle of Equivalence in General Theory of Relativity (GTR). For the case of the spherical collapse of a physical fluid, the no trapped surface condition 2GM(r, t)/R(r, t) c ²<1 was found to be required to be satisfied in all regions of spacetime, where R(r, t) is the invariant circumference variable, r is a co-moving radial coordinate and M(r, t) is the gravitational mass confined within the radius r. The above result was obtained by treating the problem from the viewpoint of an internal co-moving observer at radius r. The boundary of the fluid at r _s=R _s(r _s, t) must also behave in a similar manner, and an external stationary observer should be able to obtain a similar no trapped surface relationship. Accordingly, we generalize this analysis by studying the problem of a time-like collapsing radiating plasma from the point of view of the exterior stationary observer. We find the Principle of Equivalence implies that the physical surface surrounding the plasma must obey 1/(1+z _s)>0, where z _s is the surface red shift seen by a zero-angular momentum observer. When this condition is applied to the first integral of the time-time component of the Einstein equation, it leads to the no trapped surface condition 2GM(r _s, t)/R(r _s, t) c ²<1 consistent with the condition obtained above for the interior co-moving metric. The Principle of Equivalence enforces the no trapped surface condition by constraining the physics of the general relativistic radiation transfer process in a manner that requires it to establish and maintain an Eddington limited secular equilibrium on the dynamics of the collapsing radiating surface so as to always keep the physical surface of the collapsing object outside of its Schwarzschild radius. The important physical implication of the no trapped surface condition is that galactic black hole candidates GBHC do not possess event horizons and hence do possess intrinsic magnetic fields. In this context the spectral characteristics of galactic black hole candidates offer strong evidence that their central nuclei are highly red-shifted Magnetospheric Eternally Collapsing Objects (MECO) within the framework of General Relativity.     

Equivalence of star products on a symplectic manifold; an introduction to Deligne's Čech cohomology classes

These notes grew out of the Quantisation Seminar 1997–1998 on Deligne's paper [P. Deligne, Déformations de l'algèbre des fonctions d'une variété symplectique: Comparison entre Fedosov et De Wilde, Lecomte, Selecta Math. (New Series) 1 (1995) 667–697] and the lecture of the first author in the Workshop on Quantisation and Momentum Maps at the University of Warwich in December 1997.We recall the definitions of the cohomology classes introduced by Deligne for equivalence classes of differential star products on a symplectic manfold and show the properties of the relations between these classes by elementary methods based on Čech cohomology.     

Explicit Proof of Equivalence of Two—Point Functions in the Two Formalisms of Thermal Field Theory

We give an explicit proof of equivalence of the two-point function to one-loop order in the two formalisms of thermal λφ^3 theory based on the expressions in the real-time formalism and indicate that the key point of completing the proof is to separate carefully the imaginary part of the zero-temperature loop integral from relevant expressions and this fact will certainly be very useful for examination of the equivalent problem of two formalisms of thermal field theory in other theories,including the one of the propagators for scalar bound states in an NJL model.     

Equivalence between supersymmetric self-dual and Maxwell–Chern–Simons models coupled to a matter spinor superfield

We study the duality of the supersymmetric self-dual and Maxwell–Chern–Simons theories coupled to a fermionic matter superfield, using a master action. This approach evades the difficulties inherent to the quartic couplings that appear when matter is represented by a scalar superfield. The price is that the spinorial matter superfield represents a unusual supersymmetric multiplet, whose main physical properties we also discuss.     

Vector and Spinor Decomposition of SU（2） Gauge Potential, Their Equivalence, and Knot Structure in SU（2） Chern-Simons Theory

In this paper, spinor and vector decompositions of SU（2） gauge potential are presented and their equivalence is constructed using a simply proposal. We also obtain the action of Faddeev nonlinear 0（3） sigma model from the SU（2） mass/ve gauge field theory, which is proposed according to the gauge invariant principle. At last, the knot structure in SU（2） Chern-Simons filed theory is discussed in terms of the Φ-mapping topological current theory, The topological charge of the knot is characterized by the Hopf indices and the Brouwer degrees of Φ-mapping.