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Global correlations are widely seen in human anatomical structures due to similarity across tissues and bones. These correlations are reflected in magnetic resonance imaging (MRI) scans as a result of close-range proton density and T1/T2 parameters. Furthermore, to achieve accelerated MRI, k-space data are undersampled which causes global aliasing artifacts. Convolutional neural network (CNN) models are widely utilized for accelerated MRI reconstruction, but those models are limited in capturing global correlations due to the intrinsic locality of the convolution operation. The self-attention-based transformer models are capable of capturing global correlations among image features, however, the current contributions of transformer models for MRI reconstruction are minute. The existing contributions mostly provide CNN-transformer hybrid solutions and rarely leverage the physics of MRI. In this paper, we propose a physics-based stand-alone (convolution free) transformer model titled, the Multi-head Cascaded Swin Transformers (McSTRA) for accelerated MRI reconstruction. McSTRA combines several interconnected MRI physics-related concepts with the transformer networks: it exploits global MR features via the shifted window self-attention mechanism; it extracts MR features belonging to different spectral components separately using a multi-head setup; it iterates between intermediate de-aliasing and k-space correction via a cascaded network with data consistency in k-space and intermediate loss computations; furthermore, we propose a novel positional embedding generation mechanism to guide self-attention utilizing the point spread function corresponding to the undersampling mask. Our model significantly outperforms state-of-the-art MRI reconstruction methods both visually and quantitatively while depicting improved resolution and removal of aliasing artifacts.