A Study On The Dynamical Behaviour Of Higher-spin Gauge Fields And Scalar Fields

Gauge theory is the corner stone of modern particle physics as it provides the quantum language to describe the microscopic interactions of all fundamental particles from which all known matter,which spans from the smallest hydrogen atom to galactic matter,is formed.Although the standard model of particle physics has passed the stringent tests performed at the particle colliders,there are problems unsolved by the standard paradigm.One of the ideas is to extend the gauge bosons that mediate particle interactions in the standard model to infinitely higher spins.And therefore it is important to understand the properties of the interactions between higher spin particles.Following this line,we study the three-point amplitudes of massless particles.By assuming locality,Lorentz invariance and parity conservation,we obtain a set of differential equations governing the 3-point interactions of massless particles,which then determines the polynomial ring of the amplitudes.We derive all possible 3-point interactions for tensor and tensor-spinor fields with polarisations that have total symmetry and mixed symmetry under permutations of Lorentz indices.Constraints on the existence of gauge-invariant cubic vertices for totally symmetric fields are obtained in general spacetime dimensions and are compared with existing results obtained in the covariant and light-cone approaches.Expressing our results in spinor helicity formalism we reproduce the perhaps mysterious mismatch between the covariant approach and the light cone approach in 4 dimensions.Our analysis also shows that there exists a mismatch,in the 3-point gauge invariant amplitudes corresponding to cubic self-interactions,between a scalar field and an antisymmetric rank-2 tensor field.Despite the well-known fact that in 4 dimensions rank-2 anti-symmetric fields are dual to scalar fields in free theories,such duality does not extend to interacting theories.Scalar fields also play important roles in physics,the most famous ones among which are none other than the Higgs particle that gives fundamental particle masses and the inflaton that drives the cosmic expansion at the birth of our universe.And to properly study the early universe dynamics when particle creation is concerned,a rigorous theoretical frame of the evolution of a scalar field at finite temperature is needed.A recent work by other authors has been done to address this problem.However,the calculations were carried out in flat spacetime,not taking into consideration the effects of cosmic expansion.We extend their work by considering the evolution of a heavy scalar field ? in de Sitter spacetime to obtain the equation of motion for the expectation value of ? in a high temperature background.We assume that the Hubble parameter H is small enough such that we can calculate to the first order in H.In the closed-timepath formalism,or the “in-in formalism”,by considering the back-reaction between particles and their decay products,we calculate the self-energy and the corrections to the quartic coupling constant,leading to a temperature dependent potential and dissipation coefficient of ? in the equation of motion which contain important information about the evolution of the universe.Although the results can go back to those in flat spacetime if we set H = 0,it turns out that we need to integrate over the resonances and the effects of a nonzero H will be amplified if the coupling constants are small enough.This is a non-trivial fact that is not revealed in flat spacetime.