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"Symmetry Textbooks."
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Basic concepts of crystallography : an outcome from crystal symmetry
This textbook is based on the author's lectures.
Book
A crystallographic approach to symmetry-breaking in fluid layers
Symmetry-breaking bifurcations, where a flow state with a certain symmetry undergoes a transition to a state with a different symmetry, are ubiquitous in fluid mechanics. Much can be understood about the nature of these transitions from symmetry alone, using the theory of groups and their representations. Here, we show how the extensive databases on groups in crystallography can be exploited to yield insights into fluid dynamical problems. In particular, we demonstrate the application of the crystallographic layer groups to problems in fluid layers, using thermal convection as an example. Crystallographic notation provides a concise and unambiguous description of the symmetries involved, and we advocate its broader use by the fluid dynamics community.
Journal Article
Introduction to Renormalization Theory and Chiral Gauge Theories in Dimensional Regularization with Non-Anticommuting γ5
This review provides a detailed introduction to chiral gauge theories, renormalization theory, and the application of dimensional regularization with the non-anticommuting BMHV scheme for γ5. One goal was to show how chiral gauge theories can be renormalized despite the spurious breaking of gauge invariance and how to obtain the required symmetry-restoring counterterms. A second goal was to familiarize the reader with the theoretical basis of the renormalization of chiral gauge theories, the theorems that guarantee the existence of renormalized chiral gauge theories at all orders as consistent quantum theories. Relevant topics include BPHZ renormalization, Slavnov–Taylor identities, the BRST formalism, and algebraic renormalization, as well as the theorems guaranteeing that dimensional regularization is a consistent regularization/renormalization scheme. All of these, including their proofs and interconnections, are explained and discussed in detail. Further, these theoretical concepts are illustrated in practical applications with the example of an Abelian and a non-Abelian chiral gauge theory. Not only the renormalization procedure for such chiral gauge theories is explained step by step, but also the results of all counterterms, including the symmetry-restoring ones, necessary for the consistent renormalization, are explicitly provided.
Journal Article
Electron scattering at a potential temporal step discontinuity
We solve the problem of electron scattering at a potential temporal step discontinuity. For this purpose, instead of the Schrödinger equation, we use the Dirac equation, for access to back-scattering and relativistic solutions. We show that back-scattering, which is associated with gauge symmetry breaking, requires a vector potential, whereas a scalar potential induces only Aharonov–Bohm type energy transitions. We derive the scattering probabilities, which are found to be of later-forward and later-backward nature, with the later-backward wave being a relativistic effect, and compare the results with those for the spatial step and classical electromagnetic counterparts of the problem. Given the unrealizability of an infinitely sharp temporal discontinuity—which is of the same nature as its spatial counterpart!—we also provide solutions for a smooth potential step and demonstrate that the same physics as for the infinitely sharp case is obtained when the duration of the potential transition is sufficiently smaller than the de Broglie period of the electron (or deeply sub-period).
Journal Article
An intuitive construction of modular flow
A
bstract
The theory of modular flow has proved extremely useful for applying thermodynamic reasoning to out-of-equilibrium states in quantum field theory. However, the standard proofs of the fundamental theorems of modular flow use machinery from Fourier analysis on Banach spaces, and as such are not especially transparent to an audience of physicists. In this article, I present a construction of modular flow that differs from existing treatments. The main pedagogical contribution is that I start with thermal physics via the KMS condition, and derive the modular operator as the only operator that could generate a thermal time-evolution map, rather than starting with the modular operator as the fundamental object of the theory. The main technical contribution is a new proof of the fundamental theorem stating that modular flow is a symmetry. The new proof circumvents the delicate issues of Fourier analysis that appear in previous treatments, but is still mathematically rigorous.
Journal Article
Mathematical Geometry and Groups for Low-Symmetry Metal Complex Systems
Since chemistry, materials science, and crystallography deal with three-dimensional structures, they use mathematics such as geometry and symmetry. In recent years, the application of topology and mathematics to material design has yielded remarkable results. It can also be seen that differential geometry has been applied to various fields of chemistry for a relatively long time. There is also the possibility of using new mathematics, such as the crystal structure database, which represents big data, for computational chemistry (Hirshfeld surface analysis). On the other hand, group theory (space group and point group) is useful for crystal structures, including determining their electronic properties and the symmetries of molecules with relatively high symmetry. However, these strengths are not exhibited in the low-symmetry molecules that are actually handled. A new use of mathematics for chemical research is required that is suitable for the age when computational chemistry and artificial intelligence can be used.
Journal Article
The Influence of School Backpack Load on Dynamic Gait Parameters in 7-Year-Old Boys and Girls
School-aged children are routinely exposed to additional physical stress due to carrying school backpacks. These backpacks often exceed recommended limits and can contain not only books and notebooks but also laptops, water bottles, and other personal items. The present study aimed to evaluate the impact of different backpack loads (10%, 15%, and 20% of body weight) on dynamic gait parameters in 7-year-old girls and boys. Twenty-six children (13 girls, 13 boys) participated in the study. Gait analysis was performed using the Footscan® system (RSscan International, Olen, Belgium; 2 m × 0.4 m × 0.02 m, 16,384 sensors) equipped with Footscan software version 7 (Gait 2nd generation), examining peak force (FMAX), peak pressure (PMAX), contact area (CA), and time to peak force (Time to FMAX) across five anatomical foot zones. The study revealed significant changes in all parameters, particularly at loads of 15% and 20% of body weight. Increases in plantar pressure, contact area, and asymmetry were observed, along with delays in time to peak force. These findings support the recommendation that children’s backpack loads should not exceed 10% of their body weight to prevent potential adverse effects on postural and musculoskeletal development.
Journal Article
Symmetry and Asymmetry in Pre-Trained Transformer Models: A Comparative Study of TinyBERT, BERT, and RoBERTa for Chinese Educational Text Classification
With the advancement of educational informatization, vast amounts of Chinese text are generated across online platforms and digital textbooks. Effectively classifying such text is essential for intelligent education systems. This study conducts a systematic comparative evaluation of three Transformer-based models—TinyBERT-4L, BERT-base-Chinese, and RoBERTa-wwm-ext—for Chinese educational text classification. Using a balanced four-category subset of the THUCNews corpus (Education, Technology, Finance, and Stock), the research investigates the trade-off between classification effectiveness and computational efficiency under a unified experimental framework. The experimental results show that RoBERTa-wwm-ext achieves the highest effectiveness (93.12% Accuracy, 93.08% weighted F1), validating the benefits of whole-word masking and extended pre-training. BERT-base-Chinese maintains a balanced performance (91.74% Accuracy, 91.66% F1) with moderate computational demand. These findings reveal a clear symmetry–asymmetry dynamic: structural symmetry arises from the shared Transformer encoder and identical fine-tuning setup, while asymmetry emerges from differences in model scale and pre-training strategy. This interplay leads to distinct accuracy–latency trade-offs, providing practical guidance for deploying pre-trained language models in resource-constrained intelligent education systems.
Journal Article
Steven Weinberg’s Life for Physics
This is a personal review of Steven Weinberg’s scientific autobiography “A Life in Physics”. A reflection on both, personal aspects and scientific milestones of Professor Weinberg’s role-model life is conducted to honour his lasting accomplishments as a great physicist, academic teacher, and public activist in progressing high-energy particle theory and theoretical cosmology, and in raising public support for fundamental physics.
Journal Article
On Symmetries of Geometric Algebra Cl(3, 1) for Space-Time
From viewpoints of crystallography and of elementary particles, we explore symmetries of multivectors in the geometric algebra
Cl
(3, 1) that can be used to describe space-time.
Journal Article