Vacuum energy and the cosmological constant problem inκ-Poincaré invariant field theories

Abstract

We investigate the vacuum energy in κ-Poincaré invariant field theories. It is shown that for the equivariant Dirac operator one obtains an improvement in UV behavior of the vacuum energy and therefore the cosmological constant problem has to be revised. * Electronic address: tjuric@irb.hr † Electronic address:

$κ$-Poincaré-comodules, Braided Tensor Products and Noncommutative Quantum Field Theory

“…Another interesting issue is the relation of our construction with the approaches based on star products [33][34][35][36][38][39][40]42,[44][45][46]. In particular, [41] focuses on the lightlike κ-Minkowski spacetime, and, despite being based on a star-product approach whose fundamental ontology is that of commutative functions, it derives some results that are in line with ours so far: the free scalar QFT is undeformed, and a dependence on κ seems to be confined to the interacting theory.…”

“…There is, however, no current agreement in the literature on the correct formulation of noncommutative Quantum Field Theory (QFT), although there is a sizeable literature on the subject [33][34][35][36][37][38][39][40][41]. Recently, there has been a resurgence in interest for QFT κ-Minkowski [41][42][43][44][45][46][47][48], and perhaps the most important difference between approaches regards the basic ontology. Most approaches are based on a commutative algebra of functions, over which a non-local "star" product, involving an infinite number of derivatives of the fields, is defined.…”

Observables in Quantum Mechanics and the Importance of Self-Adjointness

“…However, when deducing the non-existence of bound states we used the assumption (73) which is not valid due to domain issues of D and Ĥ and the fact that we are missing the anomaly term (76). In Section 3.3 we have properly defined the Hamiltonian Ĥ as a SA operator on a domain with suitable boundary conditions (60), namely Ĥ := (H = − d 2 dx 2 , D α (H)) and for that operator we were able to find the bound state (68) since the new scale, the scale of symmetry breaking or anomaly came through the necessity of the parameter α which classified allowable SA boundary conditions (that is types of interaction on the boundary). Let us now calculate the anomaly (76) for our system.…”

“…Self-adjointness and the theory of SA extensions are known to play important roles in a variety of physical contexts, including systems with a confined particle [21][22][23], Aharonov-Bohm effect [24][25][26][27], graphene [28], two and three dimensional delta function potentials [29], heavy atoms [30][31][32], singular potentials [33,34], Calogero models [35,36], anyons [37,38], anomalies [39][40][41], ζ-function renormalization [42], scattering theory [43], particle statistics [44], black holes [45][46][47][48][49], integrable system [50,51], Klein-Gordon equation [52], renormalons in QM [53], quasinormal modes [54], supersymmetric QM [55] and toy models for strings [56], spectral triple [57], noncommutative field theories [58][59][60], resolving the spacetime singularities [61][62][63][64][65] and even pl...…”

Revisiting Vacuum Energy in Compact Spacetimes

“…In fact, Casimir effect has also been studied in the context of stabilizing the extra compact dimensions, early universe cosmology and also in the context of string theory. Further commentaries and investigations on all these issues and more can be looked up in [8,[30][31][32][33][34][35][36][37][38][39][40].…”