arXiv subjects
Publications and source records attributed to Holger Bech Nielsen.
Contributions of the participants of the 24th International Workshop "What Comes Beyond the Standard Models", July 5 to July 11, 2021, Bled, Slovenia, presented either with the arxiv number of each contribution or with the webside of the Proceedings published by DMFA, ZALOlZNISTVO LJUBLJANA, DECEMBER 2021.
Fifty years ago the standard model offered an elegant new step towards understanding elementary fermion and boson fields, making several assumptions, suggested by experiments. The assumptions are still waiting for an explanation. There are many proposals in the literature for the next step. The spin-charge-family theory of one of us (N.S.M.B.) is offering the explanation for not only all by the standard model assumed properties of quarks and leptons and antiquarks and antileptons, with the families included, of the vectors gauge fields, of the Higgs's scalar and Yukawa couplings, but also for the second quantization postulates of Dirac and for cosmological observations, like there are the appearance of the dark matter, of matter-antimatter asymmetry, making several predictions. This theory proposes a simple starting action in $ d\ge (13+1)$ space with fermions interacting with the gravity only, what manifests in $d=(3+1)$ as the vector and scalar gauge fields, and uses the odd Clifford algebra objects to describe the internal space of fermions, what enables that the creation and annihilation operators for fermions fulfill the anticommutation relations for the second quantized fields without Dirac's postulates: Fermions single particle states already anticommute. We present in this review article a short overview of the spin-charge-family theory, illustrating shortly on the toy model the breaks of the starting symmetries in $d=(13+1)$ space, which are triggered either by scalar fields -- the vielbeins with the space index belonging to $d>(3+1)$ -- or by the condensate of the two right handed neutrinos, with the family quantum number not belonging to the observed families. We compare properties and predictions of this theory with the properties and predictions of $SO(10)$ unifying theories.
We study the 3.55 keV X-ray suspected to arise from dark matter in our model of dark matter consisting of a bubble of a new phase of the vacuum, the surface tension of which keeps ordinary matter under high pressure inside the bubble. We consider two versions of the model: Old large pearls model : We worked for a long time on a pearl picture with pearl / bubbles of cm-size adjusted so that the impacts of them on earth could be identified with events of the mysterious type that happened in Tunguska in 1908. We fit both the very frequency, the 3.55 keV, and the overall intensity of the X-ray line coming from the center of the Milky Way and from galaxy clusters with one parameter in the model in which this radiation comes from collisions of pearls. New small pearl model: Our latest idea is to let the pearls be smaller than atoms but bigger than nuclei so as to manage to fit the 3.5 keV X-rays coming from the Tycho supernova remnant in which Jeltema and Profumo observed this line. Further we also crudely fit the DAMA-LIBRA observation with the small pearls, and even see a possibility for including the electron-recoil-excess seen by the Xenon1T experiment as being due to de-excitation via electron emission of our pearls. The important point of even our small size pearl model is that the cross section of our "macroscopic" pearls is so large that the pearls interact several times in the shielding but, due to their much larger mass than the typical nuclei, are {\bf not stopped by only a few interactions}. Nevertheless only a minute fraction of the relatively strongly interacting pearls reach the 1400 m down to the DAMA experiment, but due to the higher cross section we can fit the data anyway.
We review a bit our earlier novel string field theory\cite{self2,self8} stressing the interesting property, that it becomes expressed in terms of particle like objects called by us "objects" which in our formalism do not at all develop in time. So in this way there is in our picture, in spite of it being supposed to reproduce string theory with an arbitrary number strings present -- in this sense a string field theory -- in fact no time! This strange missing of time in the formalism gives rise to slight speculations about the philosophy of the concept of time. There is course then also no need for a Hamiltonian, but we construct or rather attempt to do so, a fake Hamiltonian or phantasy Hamiltonian,
We have constructed a new formalism for describing a situation with {\color{red} several (dual) strings} present at a time, a {\color{red} string field theory}, by means of a constituent / a strings from objects picture similar to, but importantly different from the "bits" by Charles Thorn\cite{Thorn}. Our "objects" (essentially the bits) represent rather a making a lattice in the {\color{red} light cone variables} on the string. The remarkable feature and simplicity of our formalism is, that the "objects" do {\color{red} NOT interact}, basically just run or sit trivially fixed. {\color{red} Scattering is a fake} in our formalism. This opens also up for hoping for generalizations inspired by hadrons with their partons all having Bjorken variable $x=0$, and thus infinitely many constituents. The p-adic string is an example.
In a special representation of complex action theory that we call ``future-included'', we study a harmonic oscillator model defined with a non-normal Hamiltonian $\hat{H}$, in which a mass $m$ and an angular frequency $ω$ are taken to be complex numbers. In order for the model to be sensible some restrictions on $m$ and $ω$ are required. We draw a phase diagram in the plane of the arguments of $m$ and $ω$, according to which the model is classified into several types. In addition, we formulate two pairs of annihilation and creation operators, two series of eigenstates of the Hamiltonians $\hat{H}$ and $\hat{H}^†$, and coherent states. They are normalized in a modified inner product $I_Q$, with respect to which the Hamiltonian $\hat{H}$ becomes normal. Furthermore, applying to the model the maximization principle that we previously proposed, we obtain an effective theory described by a Hamiltonian that is $Q$-Hermitian, i.e. Hermitian with respect to the modified inner product $I_Q$. The generic solution to the model is found to be the ``ground'' state. Finally we discuss what the solution implies.
We interpret anomalies, deviations, from the standard model as being in fact due to effects not given by perturbation, because the top Yukawa coupling is after all so large that not by perturbation effects become important. Most of the anomalies found have the character of signaling violation of lepton universality. There are four lepton universality violating anomalies known at present, which we shall fit with one overall scale parameter to order of magnitude accuracy. One can look at the picture that we have found - due to the rather strong top Yukawa coupling - as a new sector of strongly interacting particles analogous to quantum color dynamics inside the standard model! In addition we treat what is presumably also an anomaly: the experimental value of the direct charge conjugation parity violation parameter epsilon prime over epsilon turns out to be a factor 2 or more larger than the standard model prediction,but fit our model. However if we include in our anomaly model such processes not involving leptons (but only quarks), it seems superficially that we obtain very large - and unacceptable - anomalies in meson zero meson zero bar etc. mixing. To rescue our model from this falsification, we think of the interacting quarks as provided with clouds (on half terra electron volt scale) of, and that too strongly interacting such clouds cannot penetrate into each other. Thereby the interactions and thus the resulting anomalies are damped. Even with such a crutch for our theory we only barely manage to avoid an overlarge anomaly in the indirect charge conjugation parity violation parameter epsilon. Our modified model also predicts an anomalous contribution to the meson long to meson short mass difference of the same order of magnitude as the experimental value, which is consistent with the deviation from the standard model lattice value.
We study a complex action theory (CAT) whose path runs over not only past but also future. We show that if we regard a matrix element defined in terms of the future state at time $T_B$ and the past state at time $T_A$ as an expectation value in the CAT, then we are allowed to have the Heisenberg equation, the Ehrenfest's theorem and the conserved probability current density. In addition we show that the expectation value at the present time $t$ of a future-included theory for large $T_B-t$ and large $t- T_A$ corresponds to that of a future-not-included theory with a proper inner product for large $t- T_A$. Hence the CAT with future explicitly present in the formalism and influencing in principle the past is not excluded phenomenologically, because the effects are argued to be very small in the present era. Furthermore we explicitly derive the Schrödinger equation and Hamiltonian for the future state via path integral, and confirm that the Hamiltonian is given by the Hermitian conjugate of the Hamiltonian for the past state.
Studying the time development of the expectation value in the future-not-included complex action theory, we point out that the momentum relation (the relation analogous to $p=\frac{\partial L}{\partial \dot{q}}$), which was derived via the Feynman path integral and was shown to be correct in the future-included theory in our previous papers, is not valid in the future-not-included theory. We provide the correct momentum relation in the future-not-included theory, and argue that the future-not-included classical theory is described by a certain real action. In addition, we provide another way to understand the time development of the future-not-included theory by utilizing the future-included theory. Furthermore, properly applying the method used in our previous paper to the future-not-included theory by introducing a formal Lagrangian, we derive the correct momentum relation in the future-not-included theory.
In the complex action theory (CAT) we explicitly examine how the momentum and Hamiltonian are defined from the Feynman path integral (FPI) point of view based on the complex coordinate formalism of our foregoing paper. After reviewing the formalism briefly, we describe in FPI with a Lagrangian the time development of a $ξ$-parametrized wave function, which is a solution to an eigenvalue problem of a momentum operator. Solving this eigenvalue problem, we derive the momentum, Hamiltonian, and Schrödinger equation. Oppositely, starting from the Hamiltonian we derive the Lagrangian in FPI, and we are led to the momentum relation again via the saddle point for $p$. This study confirms that the momentum and Hamiltonian in the CAT have the same forms as those in the real action theory. We also show the third derivation of the momentum relation via the saddle point for $q$.
We have proposed a new type of string field theory. The main point of the present article is to cure some technical troubles: missing two out three terms in veneziano amplitude. Our novel string field theory, describes a theory with many strings in terms of "objects",which are not exactly, but close to Charles Thorn's string bits. The new point is that the objects in terms of which the universe states are constructed,and which have an essentially 26-momentum variable called J^μ, can have essentially the energy J^0 be also negative.We get a long way in deriving in this model the veneziano model and obtain all the three terms needed for a four point amplitude.This result strongly indicates that our novel string field theory is indeed string theory.
In quantum theory its action is usually taken to be real, but we can consider another theory whose action is complex. In addition, in the Feynman path integral, the time integration is usually performed over the period between the initial time $T_A$ and some specific time, say, the present time $t$. Besides such a future-not-included theory, we can consider the future-included theory, in which not only the past state $| A(T_A) \rangle$ at the initial time $T_A$ but also the future state $| B(T_B) \rangle$ at the final time $T_B$ is given at first, and the time integration is performed over the whole period from the past to the future. Thus quantum theory can be classified into four types, according to whether its action is real or not, and whether the future is included or not. We argue that, if a theory is described with a complex action, then such a theory is suggested to be the future-included theory, rather than the future-not-included theory. Otherwise persons living at different times would see different histories of the universe.
In the future-included complex and real action theories whose paths run over not only the past but also the future, we briefly review the theorem on the normalized matrix element of an operator $\hat{\cal O}$, which is defined in terms of the future and past states with a proper inner product $I_Q$ that makes a given Hamiltonian normal. The theorem states that, provided that the operator $\hat{\cal O}$ is $Q$-Hermitian, i.e. Hermitian with regard to the proper inner product $I_Q$, the normalized matrix element becomes real and time-develops under a $Q$-Hermitian Hamiltonian for the past and future states selected such that the absolute value of the transition amplitude from the past state to the future state is maximized. Discussing what the theorem implicates, we speculate that the future-included complex action theory would be the most elegant quantum theory.
In the future-included real action theory whose path runs over not only past but also future, we demonstrate a theorem, which states that the normalized matrix element of a Hermitian operator $\hat{\cal O}$ defined in terms of the future state at the final time $T_B$ and the fixed past state at the initial time $T_A$ becomes real for the future state selected such that the absolute value of the transition amplitude from the past state to the future state is maximized. This is a special version of our previously proposed theorem for the future-included complex action theory. We find that though the maximization principle leads to the reality of the normalized matrix element in the future-included real action theory, it does not specify the future and past states so much as in the case of the future-included complex action theory. In addition, we argue that the normalized matrix element seems to be more natural than the usual expectation value. Thus we speculate that the functional integral formalism of quantum theory could be most elegant in the future-included complex action theory.
The standard model has for massless quarks and leptons "miraculously" no triangle anomalies due to the fact that the sum of all possible traces $Tr [τ^{Ai}$$ τ^{Bj}$$ τ^{Ck}]$ --- where $τ^{Ai}, τ^{Bi}$ and $τ^{Ck}$ are the generators of one, of two or of three of the groups $SU(3), SU(2)$ and $U(1)$ --- over the representations of one family of the left handed fermions and anti-fermions (and separately of the right handed fermions and anti-fermions), contributing to the triangle currents, is equal to zero. It is demonstrated in this paper that this cancellation of the standard model triangle anomaly follows straightforwardly if the $SO(3,1), SU(2), U(1)$ and $ SU(3)$ are the subgroups of the orthogonal group $SO(13,1)$, as it is in the spin-charge-family theory. We comment on the $SO(10)$ anomaly cancellation, which works if handedness and charges are related "by hand".
We consider a rather general type of matrix model, where the matrix M represents a Hamiltonian of the interaction of a bosonic system with a single fermion. The fluctuations of the matrix are partly given by some fundamental randomness and partly dynamically, even quantum mechanically. We then study the homolumo-gap effect, which means that we study how the level density for the single-fermion Hamiltonian matrix M gets attenuated near the Fermi surface. In the case of the quenched randomness (the fundamental one) dominating the quantum mechanical one we show that in the first approximation the homolumo gap is characterized by the absence of single-fermion levels between two steep gap boundaries. The filled and empty level densities are in this first approximation just pushed, each to its side. In the next approximation these steep drops in the spectral density are smeared out to have an error-function shape. The studied model could be considered as a first step towards the more general case of considering a whole field of matrices - defined say on some phase space - rather than a single matrix.
We have long speculated \cite{1nbs,2nbs,3nbs,4nbs,5nbs, 6nbs,7nbs,8nbs,9nbs,10nbs,11nbs,12nbs, 13nbs,14nbs,LNvacuumstability} , that 6 top + 6 anti-top quarks due to the realtively large size of the top-yukawa coupling would bind exceptionaly strongly by mainly Higgs exchange. Here we present a surprisingly simple "calculation" of the mass of this speculated bound state. Even a possible resonance in scattering of two such bound states is speculated. For the "calculation" of the masses it is crucial to assume, that our since long speculated principle "Multiple Point Principle"\cite{5mp,6mp,7mp,8mp,9mp,10mp, 11mp,12mp,13mp,14mp,15mp,16mp,17mp, deriving}, is true. This principle says: {\em there are several vacua all having almost zero energy density}. Further we make an approximation of the Higgs Yukawa potential essentially replacing the exponential in it by a step-function. The new result means that there are now two independent calls for our bound state having the mass around 750 GeV required by our "new law of nature" the Multiple Point Principle. It should be remarked that in our picture there is {\em no new physics} in the sense of new fundamental particles, but the "Multiple Point Principle" is new in the sense of being not yet accepted. Further we get the {\em same} mass within uncertainties as earlier\cite{LNvacuumstability} but now from a completly different assumption, except for being from our "multiple point principle". But the two masses are gotten from using {\em different} (speculative) vacua occuring in the pure Standard Model.
In the complex action theory whose path runs over not only past but also future we study a normalized matrix element of an operator $\hat{\cal O}$ defined in terms of the future state at the latest time $T_B$ and the past state at the earliest time $T_A$ with a proper inner product that makes normal a given Hamiltonian that is non-normal at first. We present a theorem that states that, provided that the operator $\hat{\cal O}$ is $Q$-Hermitian, i.e., Hermitian with regard to the proper inner product, the normalized matrix element becomes real and time-develops under a $Q$-Hermitian Hamiltonian for the past and future states selected such that the absolute value of the transition amplitude from the past state to the future state is maximized. Furthermore, we give a possible procedure to formulate the $Q$-Hermitian Hamiltonian in terms of $Q$-Hermitian coordinate and momentum operators, and construct a conserved probability current density.