Majorana returns - MIT Center for Theoretical Physics
... this consequence as a good feature, because electrons are electrically charged, and the description of charged particles requires complex fields, even at the level of the Schrödinger equation. This is also true in the language of quantum field theory. In quantum field theory, if a given field φ crea ...
... this consequence as a good feature, because electrons are electrically charged, and the description of charged particles requires complex fields, even at the level of the Schrödinger equation. This is also true in the language of quantum field theory. In quantum field theory, if a given field φ crea ...
THE C∗-ALGEBRAIC FORMALISM OF QUANTUM MECHANICS
... to be equivalent to the more mathematically convenient Hamiltonian formalism. However, as is usually done with quantum mechanics, we immediately begin by introducing the typical axioms (i.e., where states are elements of a Hilbert space and observables are self-adjoint operators on that space), whic ...
... to be equivalent to the more mathematically convenient Hamiltonian formalism. However, as is usually done with quantum mechanics, we immediately begin by introducing the typical axioms (i.e., where states are elements of a Hilbert space and observables are self-adjoint operators on that space), whic ...
Heisenberg`s uncertainty principle in financial markets
... to photons by catalysts, i.e. not all of the energy is “radiated”, then objects emerge which can be considered as emitters of photons and have a rest mass > 0 . In order to properly define rest mass and position of rest mass, additional information of the environment Env is required, in particular ...
... to photons by catalysts, i.e. not all of the energy is “radiated”, then objects emerge which can be considered as emitters of photons and have a rest mass > 0 . In order to properly define rest mass and position of rest mass, additional information of the environment Env is required, in particular ...
Quantum Expanders: Motivation and Constructions
... the spectral gap of T is 0, and more specifically, T has |V | eigenspaces each of dimension |V |, with eigenvalues ~λ = (λ1 = 1, . . . , λ|V | ), where ~λ is the spectrum of the Cayley graph. Our first construction starts with the constant degree Ramanujan expander presented in [28]. This expander i ...
... the spectral gap of T is 0, and more specifically, T has |V | eigenspaces each of dimension |V |, with eigenvalues ~λ = (λ1 = 1, . . . , λ|V | ), where ~λ is the spectrum of the Cayley graph. Our first construction starts with the constant degree Ramanujan expander presented in [28]. This expander i ...
Quantum cryptography
... is the evolution operator that can be represented by a unitary matrix. A step of such an evolution is therefore a multiplication of a unitary matrix A with a vector |y , i.e. A |y ...
... is the evolution operator that can be represented by a unitary matrix. A step of such an evolution is therefore a multiplication of a unitary matrix A with a vector |y , i.e. A |y ...
Tensorial spacetime geometries and background
... There exist two different mathematical frameworks for the GBF called representations: The first representation called the Schrödinger representation was proposed in [54–56]. The second representation is called holomorphic representation and was established based on a mathematical rigorous framework ...
... There exist two different mathematical frameworks for the GBF called representations: The first representation called the Schrödinger representation was proposed in [54–56]. The second representation is called holomorphic representation and was established based on a mathematical rigorous framework ...
The capacity of the noisy quantum channel
... classically continuous variables such as energy, angular momentum and charge come in discrete units called quanta. This discrete character of quantum-mechanical systems such as photons, atoms, and spins allows them to register ordinary digital information. A leftcircularly polarized photon can encod ...
... classically continuous variables such as energy, angular momentum and charge come in discrete units called quanta. This discrete character of quantum-mechanical systems such as photons, atoms, and spins allows them to register ordinary digital information. A leftcircularly polarized photon can encod ...