Advancing Understanding of Matter with Quantum Electrodynamics

Precision physics aims to use atoms and molecules to test and develop the fundamental theory of matter, potentially extending beyond the Standard Model, which describes three of the four known fundamental forces in the universe. The field seeks to develop computational tools, algorithms, and equations for the most complete computation of atoms and molecules within the Quantum Electrodynamics (QED) sector. Recent developments in precision physics and spectroscopy applications have focused on the relativistic QED framework, sharing common features with the successful relativistic quantum chemistry methodology. The future of precision physics lies in the continued refinement of these tools and equations.

What is the Purpose of Precision Physics?

Precision physics is a field that aims to use atoms and molecules to test and develop the fundamental theory of matter, potentially extending beyond the Standard Model. The Standard Model is a theory in physics that describes three of the four known fundamental forces in the universe, as well as classifying all known elementary particles. Most atomic and molecular phenomena are described by the Quantum Electrodynamics (QED) sector of the Standard Model.

The goal of precision physics is to have the computational tools, algorithms, and practical equations for the most complete computation of atoms and molecules within the QED sector. The fundamental equation to start with is a topic of debate. Some argue that it is still Schrödinger’s wave equation for molecular matter, while others believe there is something beyond that.

This paper provides a concise overview of the relativistic QED framework and recent numerical developments targeting precision physics and spectroscopy applications. These developments share common features with the robust and successful relativistic quantum chemistry methodology.

How Does the Schrödinger Equation Fit into Precision Physics?

The Schrödinger equation, formulated in 1926, is a fundamental equation in quantum mechanics. The Hamiltonian in this equation is the sum of the kinetic and potential energy. From special relativity, formulated in 1905, it is known that the energy of a moving mass with momentum is given by the Einstein energy relation. This relativistic energy is the sum of the rest energy and the generalized kinetic energy, which reduces to the classical kinetic energy for velocities much lower than the speed of light in vacuum.

The total energy can also include the potential energy due to an external potential. The relativistic Hamiltonian in general is a complex equation that includes the momentum and mass of the particle, the speed of light, and the potential energy.

What is the Dirac Equation?

Paul Dirac, a British theoretical physicist, wanted to rewrite the square root in the Einstein energy relation such that the Hamiltonian is linear in momentum. When he succeeded, the result was the Dirac equation, formulated in 1928. This equation includes the one-particle Dirac Hamiltonian, the Dirac matrices, and the 4-component Dirac spinor, which represents massive spin-1/2 fermions.

The Dirac equation is the relativistic description of such spin-1/2 fermions. It can be solved for the one-electron atom where the potential energy is the time-independent external electric potential energy generated by the infinite-mass nucleus. Dirac also named the relativistic treatment of electrons Quantum Electrodynamics (QED).

What is Quantum Electrodynamics (QED)?

Quantum Electrodynamics (QED) is a theory that describes how light and matter interact. It is a fundamental theory in quantum physics and was named by Paul Dirac. QED is a key part of the Standard Model of particle physics, which describes three of the four known fundamental forces in the universe.

QED is used to describe most atomic and molecular phenomena. The goal of precision physics is to have the computational tools, algorithms, and practical equations for the most complete computation of atoms and molecules within the QED sector. This requires a deep understanding of the QED framework and the ability to apply it to practical problems.

What are the Recent Developments in Precision Physics?

Recent developments in precision physics and spectroscopy applications have focused on the relativistic QED framework. These developments share common features with the robust and successful relativistic quantum chemistry methodology.

These advancements are crucial for the continued development and testing of the fundamental theory of matter. They provide the tools and equations necessary for the most complete computation of atoms and molecules within the QED sector.

These developments are not only important for theoretical physics but also have practical applications. They can be used in spectroscopy, a tool used to study the interaction of light with matter, which has applications in many fields including chemistry, physics, and astronomy.

What is the Future of Precision Physics?

The future of precision physics lies in the continued development and refinement of computational tools, algorithms, and practical equations. These tools will allow for more precise and complete computations of atoms and molecules within the QED sector.

The field will continue to test and develop the fundamental theory of matter, potentially extending beyond the Standard Model. This will require a deep understanding of both the Schrödinger and Dirac equations, as well as the QED framework.

As the field advances, it will likely find new applications in spectroscopy and other areas. The continued development of precision physics will not only advance our understanding of the universe but also have practical applications in many scientific fields.