Algebraic formulation of the light-front vacuum

One of the main tasks of theoretical physics is to build a mathematical model which can be used to predict the outcome of experiments. The construction of a model which describes some of sort realistic event, such as two particles colliding, often starts by first specifying a function which describes empty space, usually called that vacuum state. To describe a single particle alone in the universe, one can modify the vacuum state by applying some sort of creation operator to the function that describes empty space. A system consisting of multiple particles can then described by simply applying this creation operator multiple times. Similarly, we can remove a particle from our description through the use of what is referred to as an annihilation operator. In this way, one can systematically develop a description for any number of particles by just knowing how to describe the vacuum and the process for adding or removing a particle.

For basic models, the process of constructing a mathematical model of the vacuum state, creation operator, and annihilation operator is relatively straightforward. In fact, there are several different ways in which to define these main ingredients, all of which result in equivalent prediction for the outcome of an experiment. In certain situations it it even possible to use the same description of the vacuum state with the creation and annihilation operators corresponding to different types of particles.

However, for the more advanced models, we need a framework that allows us to add an infinite number of particles to the vacuum. In these models it is necessary to carefully choose a specific vacuum state for each type of particle.

There is one description of the vacuum, called the light-front vacuum, which is compatible with a broad class of creation and annihilation operators. Models constructed using this vacuum have found great success in describing certain experiments. However, it is not really well understood why the light-front vacuum has this property, or exactly which experiments can make use of this property without requiring certain modifications.

In order to lay the groundwork necessary to understand the nature of the light-front vacuum, we examine a more abstract method of constructing both the vacuum state and the creation and annihilation operators. This method can then be applied to a simplified model which describes an infinite number of particles, each with a particular mass. By considering what happens to the models if we change the mass of the particles, we are able to gain some insight into the light-front vacuum.