Classes 20-21. Physical Foundations of Information II Quantum Field Theory Gianfranco Basti (basti@pul.va) Faculty of Philosophy – Pontifical Lateran University – www.irafs.org
IRAFS website: www.irafs.org Course: Language & Perception Syllabus I Part (1-2/11/2019) Syllabus II Part (8-9/11/2019) www.irafs.org - basti@pul.va Innopolis 2019 2
Summary ▪ We present here in a very elementary way some basic notions of the formalism of QFT, in a different framework of the classical interpretation of QFT as a “second quantization as to QM”, but in the framework of “many body physics”. This complementary way of approaching QFT allows to model quantum dissipative systems in far-from-equilibrium conditions. This a modeling is consistent with the Third Principle of Thermodynamics, allowing to give a thermodynamic interpretation of the Quantum Vacuum (QV) unavoidable fluctuations at the ground state |0 ⟩ , i.e. at the minimum of energy, however at a temperature >0°K, because of the Third Principle. This means that in QFT the fundamental physical object is not the “particle” like in quantum and classical mechanics, but the “field”, of which particles (both bosons and fermions) are their quanta or oscillating “wave-packets”. ▪ We present the main notions of QFT, allowing quantum physics to deal with “open” quantum systems in far-from-equilibrium conditions, because passing through different phases, corresponding to as many “spontaneous symmetry breakings” (SSBs) of the overall quantum field dynamics at its ground state (QV condition), and corresponding to as many long-range correlations (quantum entanglement) or phase coherence domains among the quantum fields (Goldstone Theorem) at their ground state. ▪ The dissipative QFT is therefore the fundamental physics of condensed-matter physics giving a natural microscopic explanation of macroscopic phenomena such as the phase transitions between liquid and solid phases in solid-state physics, the ferromagnetic phase in some metals, the hot superconducting phase in some ceramic materials, or, finally the morphogenesis in living matter. All these phenomena occur in far-from- equilibrium conditions, satisfying anyway an energy balance system-thermal bath (minimum of free energy), or ground state of the balanced system, compatible anyway with several ordered states of condensed matter. ▪ Since the minimum free-energy function acts here as a “dynamic”, observer-independent, selection criterion among admissible states, according to the mathematical principle of the “doubling of the degrees of freedom” system/thermal-bath, the relative notion and measure of information is here semantic, just as it is semantic the “doubled qubit” of quantum computations implemented in such a quantum architecture. ▪ This picture is completed by the possibility of modeling – by the so-called Bogoliubov Transform, mapping a condensate of photons into another one – a quantum optical system as a “labeled state-(phase)-transition-system”, i.e., as an automaton performing quantum computations at room temperature. Indeed, it is computing dynamically, like living brains as we see, through phase coherences (functions) of electromagnetic waves, and not through coherent phases of a statistical wave functions, like in the classical QM implementations of quantum computers requiring of working at temperatures � � 273 ℃ � 0°K for not suffering decoherences. ▪ Refs.: 4. 6. 7. 8. 11. 12 www.irafs.org - basti@pul.va Innopolis 2019 3
Formal Ontologies Scheme Ontology Nominalism Conceptualism Logical Realism Atomistic Natural Relational www.irafs.org - basti@pul.va Innopolis 2019 4
The standard interpretation of QFT as a «second quantization» as to QM ▪ The QFT is actually a family of theories and not only one. 1. The ordinary interpretation of QFT (OQFT) or «second quantization» is an extension of QM to many body physics developed originally by Dirac, Fock and Jordan. ▪ It is based on the indistinguishability of particles in QM, differently from CM where each particle is defined by its own position vector r i different r i’ ’s configurations different many-body states. On the contrary, in QM many particles can occupy the same quantum state (= quantum state superposition). In QM (first quantization) exchanging two particles does not change the quantum state, r i « ▪ r j , the same wave function Y is invariant for particle exchange, symmetric in the case of bosons (photons, gluons, etc.), anti-symmetric in the case of fermions (quarks, electrons, etc.): , , r , , r , , , r , , r , B i j B j i , , r , , r , , , r , , r , F i j F j i www.irafs.org - basti@pul.va Innopolis 2019 5
Vacuum state as a Fock state with occupation number equal to zero: ▪ The OQFT overcomes the difficulties intrinsic to QM for dealing with many-body systems (redundancies in defining in which state the single particle is), because the problem becomes which is the number of particles occupying the same quantum state many-body state represented in terms of occupation number of particles in the single quantum state (or Fock state ), i.e., n n n , , , n , 1 2 ▪ With 0,1 for fermions n 0,1 ,2,3... for bosons ▪ The Fock state with all occupation numbers being zero is the vacuum state |0 ñ . By applying many times the creation/annihilation operators to the vacuum state, we can add/delete as many particles to the vacuum state. ▪ All the Fock states |[ n a ] ñ form the basis of the many-body Hilbert space or Fock space any generic quantum many-body state is expressed as a linear combination of Fock states. www.irafs.org - basti@pul.va Innopolis 2019 6
The QV and the III Principle of Thermodynamics www.irafs.org - basti@pul.va Innopolis 2019 7
QV in QFT ▪ The notion of quantum vacuum QV is fundamental in QFT. This notion is the only possible explanation at the fundamental microscopic level, of the third principle of thermodynamics (“The entropy of a system approaches a constant value as the temperature approaches zero”). ▪ Indeed, the Nobel Laureate Walter Nernst, first discovered that for a given mole of matter (namely an ensemble of an Avogadro number of atoms or molecules), for temperatures close to the absolute 0, T 0 , the variation of entropy Δ S would become infinite (by dividing per 0). Namely: T T Q dT T S C C ln T T T 0 T T 0 0 Where Q is the heat transfer to the system, and C is the molar heat capacity, i.e., the total energy to be supplied to a mole for increasing its temperature by 1°C. www.irafs.org - basti@pul.va Innopolis 2019 8
QV, and the change of paradigm as to CM… ▪ Nernst demonstrated that for avoiding this catastrophe we have to suppose that C is not constant at all, but vanishes , in the limit T 0, so to make Δ S finite , as it has to be. This means however, that near the absolute 0 °K, there is a mismatch between the variation of the body content of energy, and the supply of energy from the outside. ▪ We can avoid this paradox, only by supposing that such a mysterious inner supplier of energy is the vacuum . This implies that the absolute 0° K (-273 ° C ) is unreachable. In other terms, there is an unavoidable fluctuation of the matter fields, at whichever level of matter organization. ▪ The ontological conclusion for fundamental physics is that we cannot any longer conceive physical bodies as isolated , as the inertia principle of Newtonian mechanics requires. The QV – as opposed to the mechanical vacuum of classical mechanics (CM) – plays thus the role of “inner reservoir of energy” of whichever physical system that the Third Principle of Thermodynamics necessarily requires. www.irafs.org - basti@pul.va Innopolis 2019 9
The QV in QFT as to QM ▪ Moreover, as to QM: 1. The QV at the fundamental level cannot be interpreted as a Fock state with no occupation number, and hence with a temperature 0° K like in QM and in OQFT. The QV in cosmology must be conceived with a finite temperature >0° K, even though with all energy bounded (no free energy), as required in thermodyamics. 2. The fluctuating nature of QV fields implies the necessity of supposing an infinite number of degrees of freedom in the QV coherently with the Haag Theorem in the infinite volume representation of functional analysis we have an infinite number of CCRs 3. From coherent states algebraically represented as structures defined on points (equivalently, a Schroedinger wave function within a finite «energy box») of QM to potentially infinite number of field phase coherences in the infinite volume of QV, corresponding to the infinitely many UIR’s of Haag’s theorem in QFT. www.irafs.org - basti@pul.va Innopolis 2019 10
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