Positron Emission Tomography (PET) is an established functional imaging modality integral to clinical practices. Despite its widespread utility, the attendant radiation exposure from PET scans has raised substantial health concerns. To address these challenges, numerous CNN-based methodologies have been developed to reconstruct standard-dose PET (SPET) images by using low-dose PET (LPET). These reconstructions are generally via image synthesizes using CNNs which by design, predominantly capture localized features, and thus struggle to encapsulate the long-range global feature correlations that are essential for fine-grained image synthesis. Transformers have demonstrated an inherent strength in capturing these extensive dependencies. However, the high computational and memory demands constrain its use to images at reduced resolutions, leading to potential loss of essential textural information for accurate PET synthesis. Our research proposes a new Full-resolution Transformer based model, named as Full-TrSUN, that applies a 3D transformer block at full image resolution designed to discern fine-grained, long-range dependencies. We also integrate a CNN-based encoder and decoder process in a U-Net architecture for PET image synthesis. The Full-TrSUN framework is designed to preserve the vital texture nuances at full resolution, enhancing the functional detail captured in PET synthesis. Our experimental results with public benchmark datasets show that our method outperformed the state-of-the-art methods with high efficiency.