Ghost-free infinite derivative quantum field theory

Abstract

In this paper we will study Lorentz-invariant, infinite derivative quantum field theories, where infinite derivatives give rise to non-local interactions at the energy scale M s , beyond the Standard Model. We will study a specific class, where there are no new dynamical degrees of freedom other than the original ones of the corresponding local theory. We will show that the Green functions are modified by a non-local extra term that is responsible for acausal effects, which are confined in the region of non-locality, i.e. M −1 s . The standard time-ordered structure of the causal Feynman propagator is not preserved and the non-local analog of the retarded Green function turns out to be non-vanishing for space-like separations. As a consequence the local commutativity is violated. Formulating such theories in the non-local region with Minkowski signature is not sensible, but they have Euclidean interpretation. We will show how such non-local construction ameliorates ultraviolet/short-distance singularities suffered typically in the local quantum field theory. We will show that non-locality and acausality are inherently off-shell in nature, and only quantum amplitudes are physically meaningful, so that all the perturbative quantum corrections have to be consistently taken into account. (Gaetano Lambiase), anupam.mazumdar@rug.nl (Anupam Mazumdar) 1 Quadratic curvature action contains terms like R 2 , Rµν R µν , C µνρσ Cµνρσ, where µ, ν = 0, 1, 2, 3, C stands for the Weyl tensor. In 4 dimensions one can further reduce the action with the help of Gauss-Bonnet identity.

Nonlocality amplifies echoes

“…Therefore, a crucial implication due to nonlocality is that low frequency waves survive a longer life-time as compared to the local case. This feature was expected since it is known that nonlocality weakens the interaction [6,31]. Moreover, when W n s ∼ O(1), we can also notice the presence of a turning point after which the damping time decreases.…”

“…These signatures can be potentially detectable in the context of gravitational waves, where two Dirac delta potentials can mimic the two potential barriers at the surface and at the photon sphere of an ultra compact object, or, at the two photon spheres of a wormhole, experiencing nonlocal interactions.The nonlocal interactions have been widely studied since the days of Yukawa [1], Pias and Uhlenbeck [2]. It has been studied widely in the context of quantum field theory in order to ameliorate the ultraviolet (UV) (or, in other words, short-distance) behavior of loop integrals and scattering amplitudes [3][4][5][6]. One of the striking features of nonlocality is that it weakens the interaction, and as a direct consequence it can regularize singularities through smearing out a point-like Dirac delta distribution [7][8][9][10].…”

Generalized ghost-free propagators in nonlocal field theories

“…It was also noticed that the presence of nonlocality can regularize infinities and many efforts have been made towards the resolution of black hole [17,18,[21][22][23][24][25][26][27][28][29][30][31][32][33] and cosmological [16,[34][35][36][37] singularities. At the quantum level, the high energy behavior of loop integrals has been investigated in [38][39][40][41] and properties of causality and unitarity in [42,43] and [44][45][46][47], respectively. Computations of scattering amplitudes were performed in [48][49][50], while a detailed study of spontaneous breaking of symmetry with nonlocal interactions in [51,52].…”

“…ghost modes, the number of real poles and its multiplicity cannot exceed one. For instance, one possibility in order to avoid Hamiltonian instabilities and preserve unitarity is [11,14,16,18,43] F (p 2 ) = −e γ(p 2 ) (p 2 +m 2 ) ⇒ Π(p 2 ) = e −γ(p 2 ) p 2 + m 2 , (4) whose only pole is p 2 = −m 2 since the exponential of entire function e −γ(p 2 ) does not introduce any extra zeroes in the denominator; we adopt the normalization e γ(−m 2 ) = 1, which is usually chosen [43]. Therefore, although the theory is made up of infinitely higher order derivatives, the number of degrees of freedom and also initial conditions is still finite [76,77], that is, two in this case.…”

Nonlocal gravity with worldline inversion symmetry

“…It has also been noted that nonlocality can regularise infinities, and many efforts have been made to resolve black hole [13,14,[16][17][18][19][20][21][22][23][24][25][26][27]52] and cosmological [12,[28][29][30] singularities. Furthermore, renormalisability [31][32][33], causality [34,35], unitarity [36][37][38][39][40], scattering amplitudes [41][42][43], spontaneous breaking of symmetry [44,45] and counting of initial conditions [46,47] have also been discussed and analysed. Further applications appear in the context of inflation [48], thermal field theory [49][50][51] and Galilean theories [54].…”