Quartic interaction

In quantum field theory, a quartic interaction is a type of self-interaction in a scalar field. Other types of quartic interactions may be found under the topic of four-fermion interactions. A classical free scalar field \varphi satisfies the Klein–Gordon equation. If a scalar field is denoted \varphi, a quartic interaction is represented by adding a potential energy term ({\lambda}/{4!}) \varphi^4 to the Lagrangian density. The coupling constant \lambda is dimensionless in 4-dimensional spacetime. This article uses the (+, -, -, -) metric signature for Minkowski space. The Lagrangian for a real scalar field The Lagrangian density for a real scalar field with a quartic interaction is :\mathcal{L}(\varphi)=\frac{1}{2} [\partial^\mu \varphi \partial_\mu \varphi -m^2 \varphi^2] -\frac{\lambda}{4!} \varphi^4. This Lagrangian has a global Z2 symmetry mapping \varphi\to-\varphi. The

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PHYS-416: Particle physics II

Presentation of the electroweak and strong interaction theories that constitute the Standard Model of particle physics. The course also discusses the new theories proposed to solve the problems of the Standard Model.

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José Roberto Canivete Cuissa, Daniel Garcia Figueroa

We present a lattice formulation of an interaction phi/Lambda F (F) over tilde between an axion and some U(1) gauge sector with the following properties: it reproduces the continuum theory up to O(dx(mu)(2)) corrections, it preserves exact gauge invariance and shift symmetry on the lattice, and it is suitable for self-consistent expansion of the Universe. The lattice equations of motion can no longer be solved by explicit methods, but we propose an implicit method to overcome this difficulty, which preserves the relevant system constraints down to arbitrary (tunable) precision. As a first application we study, in a comoving grid in (3 +1) dimensions, the last efolds of axion-inflation with quadratic potential and the preheating stage following afterwards. We fully account for the inhomogeneity and non-linearity of the system, including the gauge field contribution to the expansion rate of the Universe and its backreaction into the axion dynamics. We characterize in detail, as a function of the coupling, the energy transfer from the axion to the gauge field. Two coupling regimes are identified, sub- and super-critical, depending on whether the final energy fraction stored in the gauge field is below or above similar to 50% of the total energy. The Universe is very efficiently reheated for super-critical couplings, rapidly entering in a radiation dominated stage. Our results on preheating confirm previously published results.

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