Acausal Propagation Research Articles

Spontaneous symmetry breaking in models with second-class constraints

In this work the spontaneous symmetry breaking in certain nonlinear theories with second-class constraints is explored. Using the Dirac's method we perform an analysis of the constraints and the counting of the degrees of freedom. The corresponding effective Hamiltonian is constructed explicitly. It is shown that on the surfaces where the effective Hamiltonian takes critical values the symplectic structure becomes degenerate. In particular, we demonstrate that under the condition of spontaneous symmetry breaking, which implies non trivial vacuum surfaces, second-class constraints behave as first-class ones on certain regions of the phase space, leading to undefined Dirac's brackets and to the modification of the number of degrees of freedom. As a physical consequence, these models can suffer from certain pathologies such as the existence of modes with an acausal propagation. Concrete examples where this phenomena occurs are described in detail.

Second-order differential equations for bosons with spin $j \geq 1$ and in the bases of general tensor-spinors of rank 2j

A boson of spin-j>1 can be described in one of the possibilities within the Bargmann-Wigner framework by means of one sole differential equation of order twice the spin, which however is known to be inconsistent as it allows for non-local, ghost and acausally propagating solutions, all problems which are difficult to tackle. The other possibility is provided by the Fierz-Pauli framework which is based on the more comfortable to deal with second order Klein-Gordon equation, but it needs to be supplemented by an auxiliary condition. Although the latter formalism avoids some of the pathologies of the high-order equations, it still remains plagued by some inconsistencies such as the acausal propagation of the wave fronts of the (classical) solutions within an electromagnetic environment. We here suggest a method alternative to the above two that combines their advantages while avoiding the related difficulties. Namely, we suggest one sole strictly (j,0)+ (0,j) representation specific second order differential equation, which is derivable from a Lagrangian and whose solutions do not violate causality. The equation under discussion presents itself as the product of the Klein-Gordon operator with a momentum independent projector on Lorentz irreducible representation spaces constructed from one of the Casimir invariants of the spin-Lorentz group. The basis used is that of general tensor-spinors of rank-2j.

Holographic proof of the averaged null energy condition

The averaged null energy conditions (ANEC) states that, along a complete null curve, the negative energy fluctuations of a quantum field must be balanced by positive energy fluctuations. We use the AdS/CFT correspondence to prove the ANEC for a class of strongly coupled conformal field theories in flat spacetime. A violation of the ANEC in the field theory would lead to acausal propagation of signals in the bulk.

Salpeter Equation and Causality

Acausal behavior of solutions to free Salpeter equation is considered . It is shown that the formal properties of solutions suggest the acausal propagation of quantum phenomena. On the other hand the same properties of solutions describing macroscopic phenomena can be explained without appealing to the notion of acausality.

The problems in quantum foundations in the light of gauge theories

We review the issues of nonseparability and seemingly acausal propagation of information in EPR, as displayed by experiments and the failure of Bell's inequalities. We show that global effects are in the very nature of the geometric structure of modern physical theories, occurring even at the classical level. The Aharonov-Bohm effect, magnetic monopoles, instantons, etc. result from the topology and homotopy features of the fiber bundle manifolds of gauge theories. The conservation of probabilities, a supposedly highly quantum effect, is also achieved through global geometry equations. The EPR observables all fit in such geometries, and space-time is a truncated representation and is not the correct arena for their understanding. Relativistic quantum field theory represents the global action of the measurement operators as the zero-momentum (and therefore spatially infinitely spread) limit of their wave functions (form factors). We also analyze the collapse of the state vector as a case of spontaneous symmetry breakdown in the apparatus-observed state interaction.

Acausality and violation ofS-matrix unitarity for Rarita-Schwinger particles in an external electromagnetic potential

It is shown that a Rarita-Schwinger (spin 3/2) particle in an external electromagnetic field besides exhibiting acausal propagation also violates tree unitarity for semi-classical scattering. This suggests a general connection between acausal propagation and the violation of tree unitarity for high-spin (≥1) fields.

Rarita-Schwinger field in non-abelian Klein-Kaluza theories

The author deals with 3/2-spinor fields in the framework of the non-abelian Klein-Kaluza theory. He introduces a dimensional reduction procedure for a 3/2-spinor field and a generalisation of the minimal coupling scheme. He gets dipole electric moments for a 3/2-spin particle of value 10-31 cm and PC breaking for a gauge group G with odd parameters. Reflections in higher (additional) dimensions were proposed as a conjugation of 'colour' charges connected with Yang-Mills fields. His approach avoids the Velo-Zwanziger paradox (acausal propagation in an external gauge field).

On the connection between acausal propagation and the non-local structure of higher spin fields

We show that a free spin 3/2 theory of the Pauli–Fierz type displays nonlocal structure. Similarly, a spin 1 theory coupled via an electric quadrupole to an external field also shows nonlocal structure. This is in sharp contrast to the cases of spin 0, 1/2, and 1 which do not have any nonlocality even in the presence of minimal coupling to an electromagnetic field. This leads us to conjecture that the acausal propagation discovered for spin 3/2 and spin 1 is due to additional structure of these fields.

On the existence of weakly retarded and advanced Green's functions

By considering a model field equation that contains the acausal propagation features of a spin 3/2 field we show that depending on the ``external field'' one can either have weakly retarded fundamental solutions or not.

Electrodynamics and Propagation of a Spin 3/2 Field

We show that if a charged Rarita–Schwinger spin 3/2 field is coupled both to an internal as well as external electromagnetic field, acausal propagation will always occur regardless of the external field. Thus the electrodynamics of a Rarita–Schwinger spin 3/2 field is not consistent with special relativity.

Propagation of Nonlinear Electromagnetic Field Theories

It is shown that the self-interaction term λ(AμAμ)2 added to the free Lagrangian for Maxwell's equations leads to acausal propagation. Furthermore, it is found that apart from the term λAμAμ which leads back to the Proca equation, all self-interaction terms leading to causal propagation must be nonpolynomial.

Propagation of interacting fields

The spin one theory of Takahashi and Palmer [4] leads to acausal propagation when minimally coupled to an electromagnetic field. The addition of an anomalous magnetic moment (Pauli term) allows one to recover causal propagation. In the case of the Rarita-Schwinger spin 3 2 theory it is impossible to obtain causal propagation even when all possible Pauli terms are included. Coupling of a massive spin 1 2 and massive spin 1 theory leads to causal propagation for all nonderivative vector and tensor couplings, pseudo scalar and pseudo vector couplings.

The electromagnetic interaction of a massive spin one particle: some equivalence theorems and remarks

The minimal electromagnetic interaction is introduced into various free, quantum mechanical spin one formalisms, and it is found that the resulting theories are essentially equivalent. The situation does not prevail when, in addition, magnetic dipole or electric quadrupole interactions are considered. For simple such interactions in one formalism are found, in general, to be equivalent to structurally more complicated interactions in the other formalisms considered. Some known results on the acausal propagation of solutions of wave equations for a classical spin one particle in an external electromagnetic field are, with the aid of the above equivalence theorems, which are easily seen to apply to the classical case also, extended to include all the spin one formalisms considered herein.

Complex masses and acausal propagation in field theory

It is shown that in formulating a field theory with complex masses, keeping much closer to a detailed space-time description than existing treatments, one is naturally led to a modified Yang-Feldman equation. A consistent interpretation emerges, in which the complex masses are not associated with particles, but with a modification of the field propagation law, which becomes acausal. The indefinite metric of the usual treatments plays no role here. An investigation of both the case of interaction with an external potential, and of the fully quantized theory is carried out. No unitarity, or Lorentz invariance troubles arise, but in the case of a fully quantized theory, the contribution of virtual states with arbitrarily high energy, leads to an enhancement of the basic acausality of the propagation law, in a way that may lead to macroscopic deviation from causality.

Vacuum polarization of gauge-independent spin-1 field

In a recent paper (2) we have investigated the propagation of the massive spin-1 totally antisymmetric rank-two field given by TAKAHASttI and PALMER (~). Hereafter we refer to it as the T.P. field. We have found that when this field is coupled minimally to the electromagnetic field, it propagates acausally, that is some of the characteristic surfaces are spacelike. Furthermore, we have shown that by adding an appropriate dipole moment interaction to the Lagrangian, causal propagation will be recovered provided the strength of the coupling constant is equal to e, any other value will always lead to acausal propagation. This clearly indicates that the T.P. spin-1 field possesses a fixed dipole moment and does not admit an anomalous arbi trary dipole moment if causality is to be met. The fixed dipole moment interaction that we add to the T.P. minimally coupled field can be introduced in a more natural way namely, by adding a fixed four divergence to the free T.P. Lagrangian. This new Lagrangian yields causal equations of motion when minimally coupled to the electromagnetic field. We now compare the T.P. field with the well-known spin-1 Proca field. I t is known (3) that the Proea field is causal when minimally coupled to the electromagnetic field and remains so even when an arbi t rary dipole moment interaction is added to it. The Proca field, on the other hand, is not invar iant under a gauge transformation of the second kind, while the T.P. field is gauge independent (s). Thus the advantage of gauge independence restricts the T.P. field to a fixed dipole moment, while the disadvantage of noninvarianee under a gauge transformation of the second kind anows the Proca field to have an arbi t rary dipole moment without disturbing its propagation characteristics. I t is interesting to see whether the minimally coupled Proea field and the minimally coupled T.P. field with the added dipole moment which makes it causal, will yieId the same physical quantities or not. In the free case the two fields are physically indis-