Do you have an example at hand?A. Neumaier said:In particular, interacting quantum fields in 4 dimensions do not yet make mathematical sense, while physicists use them all the time.
What college do you teach physics at? I am just curious that's allA. Neumaier said:The most accurate physical theory currently known, namely QED, is not known to exist as a mathematically well-defined conceptual framework. The reason is that there is so far no logically consistent definition of a quantum field for which the physicist's (renormalized) QED interaction has been proved to exist. QCD, weak interactions, or the standard model are other examples.
On the other hands, the quantum fields considered in solid state theory, have a solid mathematical existence. They describe the deformation of crystals, currents in metals, and the like.
Then how do you know stuff about QM? Did you get your PhD in physics?A. Neumaier said:I teach mathematics. Type my name into Google to find out.
Thank you.A. Neumaier said:The most accurate physical theory currently known, namely QED, is not known to exist as a mathematically well-defined conceptual framework. The reason is that there is so far no logically consistent definition of a quantum field for which the physicist's (renormalized) QED interaction has been proved to exist. QCD, weak interactions, or the standard model are other examples.
On the other hands, the quantum fields considered in solid state theory, have a solid mathematical existence. They describe the deformation of crystals, currents in metals, and the like.
Quantum Field Theory (QFT) is a theoretical framework that combines the principles of quantum mechanics with special relativity. It describes the behavior of particles at a fundamental level by treating them as excitations in a quantum field. In this way, it provides a more complete understanding of the interactions between particles and their underlying fields.
Quantum fields can be excited by adding energy to them through interactions with other particles. This excitation can lead to the creation of new particles, as well as changes in the properties and behavior of existing particles. The implications of this excitation are far-reaching and can help explain a wide range of physical phenomena, from the behavior of subatomic particles to the properties of matter and energy at the largest scales.
A physical excitation of a quantum field refers to the actual change in the state of the field caused by the interaction with other particles. This results in the creation or modification of particles and their properties. On the other hand, a mathematical excitation is a theoretical concept used to describe the behavior of the field and its interactions, often through mathematical equations and models. Both types of excitations are important in understanding the behavior of quantum fields.
QFT describes particles as excitations of underlying quantum fields. These fields are constantly fluctuating and interacting with each other, leading to the creation and annihilation of particles. The interactions between particles are described by the exchange of virtual particles, which are excitations in the underlying fields. This framework provides a more complete and unified understanding of particle behavior and interactions compared to classical physics.
QFT has a wide range of applications in modern physics, including particle physics, condensed matter physics, and cosmology. It has been used to explain and predict the behavior of subatomic particles, the properties of matter and energy at the smallest scales, and the evolution of the universe. It also has practical applications in technologies such as transistors, lasers, and superconductors. Additionally, QFT has led to the development of important mathematical tools and methods used in many fields of science and engineering.