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Quantum Field Theory

  1. Combining Relativity and Quantum Theory (
      "The two major physics discoveries of the first part of this century, quantum mechanics and Einstein's theory of special relativity present new challenges when treated together. The energy "uncertainty" introduced in quantum theory combines with the mass-energy equivalence of special relativity to allow the creation of particle/anti-particle pairs by quantum fluctuations when the theories are merged. As a result there is no self-consistent theory which generalizes the simple, one-particle Schrödinger equation into a relativistic quantum wave equation."

      "The most successful approach to this problem, developed in the early 30's, begins not with a single relativistic particle, but with a relativistic classical field theory, such as Maxwell's theory of electromagnetism. This classical field theory is then "quantized" in the usual way and the resulting quantum field theory realizes a consistent combination of quantum mechanics and relativity. However, this theory is inherently a many-body theory with the quanta of the normal modes of the classical field having all the properties of physical particles." 01-06

  2. Quantum Field Theory (
      "The framework in which quantum mechanics and special relativity are successfully reconciled is called quantum field theory. It is based on three basic principles: two of them, of course, are quantum mechanics and special relativity. The third one, which I wish to emphasize, is the postulate that elementary particles are point-like objects of zero intrinsic size. In practice, they are smeared over a region of space due to quantum effects, but their descripton in the basic equations is as mathematical points." 01-06

  3. Quantum Field Theory (
      "Quantum field theory (QFT) is the application of quantum mechanics to fields. It provides a theoretical framework, widely used in particle physics and condensed matter physics, in which to formulate consistent quantum theories of many-particle systems, especially in situations where particles may be created and destroyed. Non-relativistic quantum field theories are needed in condensed matter physics— for example in the BCS theory of superconductivity. Relativistic quantum field theories are indispensable in particle physics (see the standard model), although they are known to arise as effective field theories in condensed matter physics." 01-06

  4. Quantum Field Theory and Quantum Gravity (
      "The revelation that particle interactions, the most basic events in nature, may be consequences of geometry significantly advances a decades-long effort to reformulate quantum field theory, the body of laws describing elementary particles and their interactions. Interactions that were previously calculated with mathematical formulas thousands of terms long can now be described by computing the volume of the corresponding jewel-like “amplituhedron,” which yields an equivalent one-term expression."

      "The new geometric version of quantum field theory could also facilitate the search for a theory of quantum gravity that would seamlessly connect the large- and small-scale pictures of the universe. Attempts thus far to incorporate gravity into the laws of physics at the quantum scale have run up against nonsensical infinities and deep paradoxes. The amplituhedron, or a similar geometric object, could help by removing two deeply rooted principles of physics: locality and unitarity." 09-13


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